Log in

Relevant bibliographies by topics / Wielandt subgroup / Journal articles

Journal articles on the topic 'Wielandt subgroup'

To see the other types of publications on this topic, follow the link: Wielandt subgroup.

Author: Grafiati

Published: 4 June 2021

Last updated: 28 January 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 41 journal articles for your research on the topic 'Wielandt subgroup.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Cossey, John. "The Wielandt subgroup of a polycyclic group." Glasgow Mathematical Journal 33, no. 2 (May 1991): 231–34. http://dx.doi.org/10.1017/s0017089500008260.

Full text

Abstract:

The purpose of this paper is to establish some basic properties of the Wielandt subgroup of a polycyclic group. The Wielandt subgroup of a group G is defined to be the intersection of the normalisers of all the subnormal subgroups of G and is denoted by ω(G). In 1958 Wielandt [9] showed that any minimal normal subgroup with the minimum condition on subnormal subgroups is contained in the Wielandt subgroup: it follows that the Wielandt subgroup of an artinian group is nontrivial. In contrast, the Wielandt subgroup of a polycyclic group can be trivial; an easy example is given by the infinite dihedral group. We will show that the Wielandt subgroup of a polycyclic group is close to being central.

APA, Harvard, Vancouver, ISO, and other styles

2

Ormerod, Elizabeth A. "Groups of Wielandt length two." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 2 (September 1991): 229–44. http://dx.doi.org/10.1017/s0305004100070304.

Full text

Abstract:

The Wielandt subgroup ω(G) of a group G is the subgroup of elements that normalize every subnormal subgroup of G. This subgroup, now named for Wielandt, was introduced by him in 1958 [15]. For a finite non-trivial group the Wielandt subgroup is always a non-trivial, characteristic subgroup. Thus it is possible to define the ascending Wielandt series for a finite group G which terminates at the group. Write ω0(G) = 1, and for i ≥ 1, ωi(G)/ωi–1(G) = ω(G/ωi–1(G)). The smallest n such that ωn(G) = G is called the Wielandt length of G, and the class of groups of Wielandt length at most n is denoted by . From the definition it follows that is closed under homomorphic images and taking normal subgroups. Nilpotent groups in are also closed under taking subgroups.

APA, Harvard, Vancouver, ISO, and other styles

3

Bryce, R. A., John Cossey, and E. A. Ormerod. "A note on p-groups with power automorphisms." Glasgow Mathematical Journal 34, no. 3 (September 1992): 327–32. http://dx.doi.org/10.1017/s0017089500008892.

Full text

Abstract:

Let G be a group. The norm, or Kern of G is the subgroup of elements of G which normalize every subgroup of the group. This idea was introduced in 1935 by Baer [1, 2], who delineated the basic properties of the norm. A related concept is the subgroup introduced by Wielandt [10] in 1958, and now named for him. The Wielandt subgroup of a group G is the subgroup of elements normalizing every subnormal subgroup of G. In the case of finite nilpotent groups these two concepts coincide, of course, since all subgroups of a finite nilpotent group are subnormal. Of late the Wielandt subgroup has been widely studied, and the name tends to be the more used, even in the finite nilpotent context when, perhaps, norm would be more natural. We denote the Wielandt subgroup of a group G by ω(G). The Wielandt series of subgroups ω1(G) is defined by: ω1(G) = ω(G) and for i ≥ 1, ωi+1(G)/ ω(G) = ω(G/ωi, (G)). The subgroups of the upper central series we denote by ζi(G).

APA, Harvard, Vancouver, ISO, and other styles

4

Ormerod, Elizabeth A. "The Wielandt subgroup of metacyclic p-groups." Bulletin of the Australian Mathematical Society 42, no. 3 (December 1990): 499–510. http://dx.doi.org/10.1017/s0004972700028665.

Full text

Abstract:

The Wielandt subgroup is the intersection of the normalisers of all the subnormal subgroups of a group. For a finite group it is a non-trivial characteristic subgroup, and this makes it possible to define an ascending normal series terminating at the group. This series is called the Wielandt series and its length determines the Wielandt length of the group. In this paper the Wielandt subgroup of a metacyclic p–group is identified, and using this information it is shown that if a metacyclic p–group has Wielandt length n, its nilpotency class is n or n + 1.

APA, Harvard, Vancouver, ISO, and other styles

5

Ali, A. "On the Wielandt length of a finite supersoluble group." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 6 (December 2000): 1217–26. http://dx.doi.org/10.1017/s0308210500000640.

Full text

Abstract:

We develop a technique for calculating the Wielandt subgroup of a semidirect product of two finite groups of coprime order. We apply this technique to calculate the Wielandt length of a supersoluble group in terms of the Wielandt lengths of its Sylow subgroups (for small Wielandt lengths) and in terms of the nilpotency classes of its Sylow subgroups.

APA, Harvard, Vancouver, ISO, and other styles

6

Brandl, Rolf, Silvana Franciosi, and Francesco de Giovanni. "On the Wielandt subgroup of infinite soluble groups." Glasgow Mathematical Journal 32, no. 2 (May 1990): 121–25. http://dx.doi.org/10.1017/s0017089500009149.

Full text

Abstract:

The Wielandt subgroup w(G) of a group G is defined to be the intersection of the normalizers of all the subnormal subgroups of G. If G is a group satisfying the minimal condition on subnormal subgroups then Wielandt [10] showed that w(G) contains every minimal normal subgroup of G, and so contains the socle of G, and, later, Robinson [6] and Roseblade [9] proved that w(G) has finite index in G.

APA, Harvard, Vancouver, ISO, and other styles

7

Casolo, Carlo. "Soluble Groups with Finite Wielandt length." Glasgow Mathematical Journal 31, no. 3 (September 1989): 329–34. http://dx.doi.org/10.1017/s0017089500007898.

Full text

Abstract:

The Wielandt subgroup ω(G) of a group G is defined to be the intersection of all normalizers of subnormal subgroups of G; the terms of the Wielandt series of G are defined, inductively, by putting ω0(G) = 1 and (ωn+1(G)/ωn(G) = ω(G/ωn(G)). If, for some integer n, ωn(G) = G, then G is said to have finite Wielandt length; the Wielandt length of G being the minimal n such that ωn(G) = G.

APA, Harvard, Vancouver, ISO, and other styles

8

Ormerod, Elizabeth A. "Some p-groups of Weilandt length three." Bulletin of the Australian Mathematical Society 58, no. 1 (August 1998): 121–36. http://dx.doi.org/10.1017/s0004972700032056.

Full text

Abstract:

Finite p-groups of Wielandt length 1 are groups in which every subgroup is normal and are Dedekind groups. When the prime is odd therefore a finite p-group of Wielandt length 1 is Abelian. For an odd prime, a finite p-group of Wielandt length 2 has nilpotency class at most 3 and for such a goup to have class 3 there must be a 2-generator subgroup of this class. In this paper it is shown that for any prime p > 3 a finite p-group of Wielandt length 3 has nilpotency class at most 4, and for such a group to have class 4 there must be a 2-generator subgroup with this class. Two families of p-groups of Wielandt length 3 are described. One is a family of 3-generator groups with the property that each group modulo its Wielandt subgroup has class 2, the other is a family of 2-generator groups with the property that each group modulo its Wielandt subgroup has class 3.

APA, Harvard, Vancouver, ISO, and other styles

9

Beidleman, James C., Martyn R. Dixon, and Derek J. S. Robinson. "The Generalized Wielandt Subgroup of a Group." Canadian Journal of Mathematics 47, no. 2 (April 1, 1995): 246–61. http://dx.doi.org/10.4153/cjm-1995-012-7.

Full text

Abstract:

AbstractThe intersection IW(G) of the normalizers of the infinite subnormal subgroups of a group G is a characteristic subgroup containing the Wielandt subgroup W(G) which we call the generalized Wielandt subgroup. In this paper we show that if G is infinite, then the structure of IW(G)/ W(G) is quite restricted, being controlled by a certain characteristic subgroup S(G). If S(G) is finite, then so is IW(G)/ W(G), whereas if S(G) is an infinite Prüfer-by-finite group, then IW(G)/W(G) is metabelian. In all other cases, IW(G) = W(G).

APA, Harvard, Vancouver, ISO, and other styles

10

Wetherell, C. J. T. "The wielandt series of metabelian groups." Bulletin of the Australian Mathematical Society 67, no. 2 (April 2003): 267–76. http://dx.doi.org/10.1017/s0004972700033736.

Full text

Abstract:

The Wielandt subgroup of a group is the intersection of the normalisers of its subnormal subgroups. It is non-trivial in any finite group and thus gives rise to a series whose length provides a measure of the complexity of the group's subnormal structure. In this paper results of Ormerod concerning the interplay between the Wielandt series and upper central series of metabelian p-groups, p odd, are extended to the class of all odd order metabelian groups. These extensions are formulated in terms of a natural generalization of the upper central series which arises from Casolo's strong Wielandt subgroup, the intersection of the centralisers of a group's nilpotent subnormal sections.

APA, Harvard, Vancouver, ISO, and other styles

11

SU, NING, and YANMING WANG. "ON THE -LENGTH AND THE WIELANDT SERIES OF A FINITE -SOLUBLE GROUP." Bulletin of the Australian Mathematical Society 91, no. 2 (December 9, 2014): 219–26. http://dx.doi.org/10.1017/s0004972714000872.

Full text

Abstract:

AbstractThe Wielandt subgroup of a group $G$, denoted by ${\it\omega}(G)$, is the intersection of the normalisers of all subnormal subgroups of $G$. The terms of the Wielandt series of $G$ are defined, inductively, by putting ${\it\omega}_{0}(G)=1$ and ${\it\omega}_{i+1}(G)/{\it\omega}_{i}(G)={\it\omega}(G/{\it\omega}_{i}(G))$. In this paper, we investigate the relations between the$p$-length of a $p$-soluble finite group and the Wielandt series of its Sylow $p$-subgroups. Some recent results are improved.

APA, Harvard, Vancouver, ISO, and other styles

12

Franchi, Clara. "m-Wielandt series in infinite groups." Journal of the Australian Mathematical Society 70, no. 1 (February 2001): 76–87. http://dx.doi.org/10.1017/s1446788700002299.

Full text

Abstract:

AbstractIn a group G, um (G) denotes the subgroup of the elements which normalize every subnormal subgroup of G with defect at most m. The m-Wielandt series of G is then defined in a natural way. G is said to have finite m-Wielandt length if it coincides with a term of its m-Wielandt series. We investigate the structure of infinite groups with finite m-Wielandt length.

APA, Harvard, Vancouver, ISO, and other styles

13

Malinowska, Izabela Agata. "Finite groups in which normality, permutability or Sylow permutability is transitive." Analele Universitatii "Ovidius" Constanta - Seria Matematica 22, no. 3 (September 1, 2014): 137–46. http://dx.doi.org/10.2478/auom-2014-0055.

Full text

Abstract:

AbstractY. Li gave a characterization of the class of finite soluble groups in which every subnormal subgroup is normal by means of NE-subgroups: a subgroup H of a group G is called an NE-subgroup of G if NG(H) ∩ HG = H. We obtain a new characterization of these groups related to the local Wielandt subgroup. We also give characterizations of the classes of finite soluble groups in which every subnormal subgroup is permutable or Sylow permutable in terms of NE-subgroups.

APA, Harvard, Vancouver, ISO, and other styles

14

Kaplan, G., and G. Vincenzi. "On the Wielandt subgroup of generalized FC-groups." International Journal of Algebra and Computation 24, no. 07 (November 2014): 1031–42. http://dx.doi.org/10.1142/s0218196714500441.

Full text

Abstract:

We extend to soluble FC*-groups, the class of generalized FC-groups introduced in [de Giovanni, Russo and Vincenzi, Groups with restricted conjugacy classes, Serdica Math. J. 28(3) (2002) 241–254], the characterization of finite soluble T-groups, and some results on the Wielandt subgroup, obtained recently in [Kaplan, On finite T-groups and the Wielandt subgroup, J. Group Theory. 14 (2011) 855–863].

APA, Harvard, Vancouver, ISO, and other styles

15

Kaplan, Gil. "A note on Frobenius–Wielandt groups." Journal of Group Theory 22, no. 4 (July 1, 2019): 637–45. http://dx.doi.org/10.1515/jgth-2018-0140.

Full text

Abstract:

AbstractLet G be a finite group. G is called a Frobenius–Wielandt group if there exists {H<G} such that {U=\langle H\cap H^{g}\mid g\in G-H\rangle} is a proper subgroup of H. The Wielandt theorem [H. Wielandt, Über die Existenz von Normalteilern in endlichen Gruppen, Math. Nachr. 18 1958, 274–280; Mathematische Werke Vol. 1, 769–775] on the structure of G generalizes the celebrated Frobenius theorem. From a permutation group point of view, considering the action of G on the coset space {G/H}, it states in particular that the subgroup {D=D_{G}(H)} generated by all derangements (fixed-point-free elements) is a proper subgroup of G. Let {W=U^{G}}, the normal closure of U in G. Then W is the subgroup generated by all elements fixing at least two points. We present the proof of the Wielandt theorem in a new way (Theorem 1.6, Corollary 1.7, Theorem 1.8) such that the unique component whose proof is not elementary or by the Frobenius theorem is the equality {W\cap H=U}. This presentation shows what can be achieved by elementary arguments and how Frobenius groups are involved in one case of Frobenius–Wielandt groups. To be more precise, Theorem 1.6 shows that there are two possible cases for a Frobenius–Wielandt group G with {H<G}: (a) {W=D} and {G=HW}, or (b) {W<D} and {HW<G}. In the latter case, {G/W} is a Frobenius group with a Frobenius complement {HW/W} and Frobenius kernel {D/W}.

APA, Harvard, Vancouver, ISO, and other styles

16

Franciosi, Silvana, Francesco de Giovanni, and Yaroslav P. Sysak. "An extension of the Kegel–Wielandt theorem to locally finite groups." Glasgow Mathematical Journal 38, no. 2 (May 1996): 171–76. http://dx.doi.org/10.1017/s0017089500031402.

Full text

Abstract:

A famous theorem of Kegel and Wielandt states that every finite group which is the product of two nilpotent subgroups is soluble (see [1], Theorem 2.4.3). On the other hand, it is an open question whether an arbitrary group factorized by two nilpotent subgroups satisfies some solubility condition, and only a few partial results are known on this subject. In particular, Kegel [6] obtained an affirmative answer in the case of linear groups, and in the same article he also proved that every locally finite group which is the product of two locally nilpotent FC-subgroups is locally soluble. Recall that a group G is said to be an FC-group if every element of G has only finitely many conjugates. Moreover, Kazarin [5] showed that if the locally finite group G = AB is factorized by an abelian subgroup A and a locally nilpotent subgroup B, then G is locally soluble. The aim of this article is to prove the following extension of the Kegel–Wielandt theorem to locally finite products of hypercentral groups.

APA, Harvard, Vancouver, ISO, and other styles

17

Espuelas, Alberto. "A nonabelian Frobenius–Wielandt complement." Proceedings of the Edinburgh Mathematical Society 31, no. 1 (February 1988): 67–69. http://dx.doi.org/10.1017/s001309150000657x.

Full text

Abstract:

We recall the following definition (see [1]):A finite group G is said to be a Frobenius–Wielandt group provided that there exists a proper subgroup H of G and a proper normal subgroup N of H such that H∩Hg≦N if g∈G–H. Then H/N is said to be the complement of (G, H, N) (see [1] for more details and notation).

APA, Harvard, Vancouver, ISO, and other styles

18

Ballester-Bolinches, A., and L. M. Ezquerro. "A NOTE ON FINITE GROUPS GENERATED BY THEIR SUBNORMAL SUBGROUPS." Proceedings of the Edinburgh Mathematical Society 44, no. 2 (June 2001): 417–23. http://dx.doi.org/10.1017/s0013091500000018.

Full text

Abstract:

AbstractFollowing the theory of operators created by Wielandt, we ask for what kind of formations $\mathfrak{F}$ and for what kind of subnormal subgroups $U$ and $V$ of a finite group $G$ we have that the $\mathfrak{F}$-residual of the subgroup generated by two subnormal subgroups of a group is the subgroup generated by the $\mathfrak{F}$-residuals of the subgroups.In this paper we provide an answer whenever $U$ is quasinilpotent and $\mathfrak{F}$ is either a Fitting formation or a saturated formation closed for quasinilpotent subnormal subgroups.AMS 2000 Mathematics subject classification: Primary 20F17; 20D35

APA, Harvard, Vancouver, ISO, and other styles

19

ROMANO, E., and G. VINCENZI. "PRONORMALITY IN GENERALIZED FC-GROUPS." Bulletin of the Australian Mathematical Society 83, no. 2 (September 14, 2010): 220–30. http://dx.doi.org/10.1017/s0004972710001668.

Full text

Abstract:

AbstractWe extend some results known for FC-groups to the class FC* of generalized FC-groups introduced in de Giovanni et al. [‘Groups with restricted conjugacy classes’, Serdica Math. J.28(3) (2002), 241–254]. The main theorems pertain to the join of pronormal subgroups. The relevant role that the Wielandt subgroup plays in an FC*-group is pointed out.

APA, Harvard, Vancouver, ISO, and other styles

20

Bryce, R. A., and John Cossey. "The Wielandt Subgroup of a Finite Soluble Group." Journal of the London Mathematical Society s2-40, no. 2 (October 1989): 244–56. http://dx.doi.org/10.1112/jlms/s2-40.2.244.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Guo, Xiuyun, and Xiaohong Zhang. "On the Norm and Wielandt Series in Finite Groups." Algebra Colloquium 19, no. 03 (July 5, 2012): 411–26. http://dx.doi.org/10.1142/s1005386712000272.

Full text

Abstract:

The norm N(G) of a group G is the intersection of the normalizes of all the subgroups of G. A group is called capable if it is a central factor group. In this paper, we give a necessary and sufficient condition for a capable group to satisfy N(G)=ζ(G), and then some sufficient conditions for a capable group with N(G)=ζ(G) are obtained. Furthermore, we discuss the norm of a nilpotent group with cyclic derived subgroup.

APA, Harvard, Vancouver, ISO, and other styles

22

Dixon, Martyn R., Maria Ferrara, and Marco Trombetti. "An analogue of the Wielandt subgroup in infinite groups." Annali di Matematica Pura ed Applicata (1923 -) 199, no. 1 (June 11, 2019): 253–72. http://dx.doi.org/10.1007/s10231-019-00876-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Ballester-Bolinches, A., S. F. Kamornikov, and V. Pérez-Calabuig. "On formations of finite groups with the generalized Wielandt property for residuals II." Journal of Algebra and Its Applications 17, no. 09 (August 23, 2018): 1850167. http://dx.doi.org/10.1142/s0219498818501670.

Full text

Abstract:

A formation [Formula: see text] of finite groups has the generalized Wielandt property for residuals, or [Formula: see text] is a GWP-formation, if the [Formula: see text]-residual of a group generated by two [Formula: see text]-subnormal subgroups is the subgroup generated by their [Formula: see text]-residuals. The main result of this paper describes a large family of GWP-formations to further the transparence of this kind of formations, and it can be regarded as a natural step toward the solution of the classification problem.

APA, Harvard, Vancouver, ISO, and other styles

24

Ormerod, Elizabeth A. "A note on the wielandt subgroup of a metabelianp-group." Communications in Algebra 27, no. 2 (January 1999): 621–27. http://dx.doi.org/10.1080/00927879908826452.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Zhang, Xiaohong, and Xiuyun Guo. "On the wielandt subgroup in a p-group of maximal class." Chinese Annals of Mathematics, Series B 33, no. 1 (January 2012): 83–90. http://dx.doi.org/10.1007/s11401-011-0690-z.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Cameron, P., and K. W. Johnson. "An investigation of countable B-groups." Mathematical Proceedings of the Cambridge Philosophical Society 102, no. 2 (September 1987): 223–31. http://dx.doi.org/10.1017/s0305004100067256.

Full text

Abstract:

A group G is defined to be a B-group if any primitive permutation group which contains G as a regular subgroup is doubly transitive. In the case where G is finite the existence of families of B-groups has been established by Burnside, Schur, Wielandt and others and led to the investigation of S-rings. A survey of this work is given in [3], sections 13·7–13·12. In this paper the possibility of the existence of countable B-groups is discussed. Three distinct methods are given to embed a countable group as a regular subgroup of a simply primitive permutation group, and in each case a condition on the square root sets of elements of the group is necessary for the embedding to be carried out. It is easy to demonstrate that this condition is not sufficient, and the general question remains open.

APA, Harvard, Vancouver, ISO, and other styles

27

Franchi, Clara. "Subgroups like Wielandt's in soluble groups." Glasgow Mathematical Journal 42, no. 1 (March 2000): 67–74. http://dx.doi.org/10.1017/s0017089500010090.

Full text

Abstract:

For each m≥1, u_{m}(G) is defined to be the intersection of the normalizers of all the subnormal subgroups of defect at most m in G. An ascending chain of subgroups u_{m,i}(G) is defined by setting u_{m,i}(G)/u_{m,i−1}(G)=u_{m}(G/u_{m,i−1}(G)). If u_{m,n}(G)=G, for some integer n, the m-Wielandt length of G is the minimal of such n.In [3], Bryce examined the structure of a finite soluble group with given m-Wielandt length, in terms of its polynilpotent structure. In this paper we extend his results to infinite soluble groups.1991 Mathematics Subject Classification. 20E15, 20F22.

APA, Harvard, Vancouver, ISO, and other styles

28

Bryce, R. A. "Subgroups like Wielandt's in finite soluble groups." Mathematical Proceedings of the Cambridge Philosophical Society 107, no. 2 (March 1990): 239–59. http://dx.doi.org/10.1017/s0305004100068511.

Full text

Abstract:

In 1935 Baer[1] introduced the concept of kern of a group as the subgroup of elements normalizing every subgroup of the group. It is of interest from three points of view: that of its structure, the nature of its embedding in the group, and the influence of its internal structure on that of the whole group. The kern is a Dedekind group because all its subgroups are normal. Its structure is therefore known exactly (Dedekind [7]): if not abelian it is a direct product of a copy of the quaternion group of order 8 and an abelian periodic group with no elements of order 4. As for the embedding of the kern, Schenkman[13] shows that it is always in the second centre of the group: see also Cooper [5], theorem 6·5·1. As an example of the influence of the structure of the kern on its parent group we cite Baer's result from [2], p. 246: among 2-groups, only Hamiltonian groups (i.e. non-abelian Dedekind groups) have nonabelian kern.

APA, Harvard, Vancouver, ISO, and other styles

29

Revin, Danila, Saveliy Skresanov, and Andrey Vasil’ev. "The Wielandt–Hartley theorem for submaximal $$\mathfrak {X}$$-subgroups." Monatshefte für Mathematik 193, no. 1 (June 5, 2020): 143–55. http://dx.doi.org/10.1007/s00605-020-01425-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Chin, A. Y. M., and Angeline P. L. Lee. "A Characterization of Higher Order Wielandt Subgroups and Some Applications." Missouri Journal of Mathematical Sciences 21, no. 3 (October 2009): 206–9. http://dx.doi.org/10.35834/mjms/1316024886.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Kleidman, Peter B. "A Proof of the Kegel-Wielandt Conjecture on Subnormal Subgroups." Annals of Mathematics 133, no. 2 (March 1991): 369. http://dx.doi.org/10.2307/2944342.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Flavell, Paul. "On Wielandt's theory of subnormal subgroups." Bulletin of the London Mathematical Society 42, no. 2 (April 2010): 263–66. http://dx.doi.org/10.1112/blms/bdp122.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

SU, NING, and YANMING WANG. "ON THE -LENGTH AND THE WIELANDT LENGTH OF A FINITE -SOLUBLE GROUP." Bulletin of the Australian Mathematical Society 88, no. 3 (March 7, 2013): 453–59. http://dx.doi.org/10.1017/s0004972713000026.

Full text

Abstract:

AbstractThe $p$-length of a finite $p$-soluble group is an important invariant parameter. The well-known Hall–Higman $p$-length theorem states that the $p$-length of a $p$-soluble group is bounded above by the nilpotent class of its Sylow $p$-subgroups. In this paper, we improve this result by giving a better estimation on the $p$-length of a $p$-soluble group in terms of other invariant parameters of its Sylow $p$-subgroups.

APA, Harvard, Vancouver, ISO, and other styles

34

Smith, Howard. "Groups with the Subnormal Join Property." Canadian Journal of Mathematics 37, no. 1 (February 1, 1985): 1–16. http://dx.doi.org/10.4153/cjm-1985-001-8.

Full text

Abstract:

A group G is said to have the subnormal join property (s.j.p.) if the join of two (and hence of finitely many) subnormal subgroups of G is always subnormal in G. Following Robinson [6], we shall denote the class of groups having this property by . A particular subclass of is , consisting of those groups G in which the join of two subnormals is again subnormal in G and has defect bounded in terms of the defects of the constituent subgroups (for a more precise definition see Section 7 of [6]).In [16], Wielandt showed that groups which satisfy the maximal condition for subnormal subgroups have the s.j.p. Many further results on groups with the s.j.p. were proved in [6] and [7]. In Sections 2 and 3 of this paper, it will be shown that several of these results can be exhibited as corollaries of a few rather more general theorems on the classes , .

APA, Harvard, Vancouver, ISO, and other styles

35

Ballester-Bolinches, Adolfo. "$\mathfrak{F}$ -critical groups, $\mathfrak{F}$ -subnormal subgroups, and the generalised Wielandt property for residuals." Ricerche di Matematica 55, no. 1 (July 2006): 13–30. http://dx.doi.org/10.1007/s11587-006-0002-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Kaplan, Gil. "On finite T-groups and the Wielandt subgroup." Journal of Group Theory 14, no. 6 (January 1, 2011). http://dx.doi.org/10.1515/jgt.2011.082.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Cao, Huiqin, and Jiwen Zeng. "A note on modular Frobenius groups." Journal of Algebra and Its Applications, October 12, 2020, 2250020. http://dx.doi.org/10.1142/s0219498822500207.

Full text

Abstract:

It is well known that Frobenius groups can be defined by their complement subgroups. But until now we cannot use a complement subgroup to define a modular Frobenius group. In the present paper, a generalization of Frobenius complements is used as a characterization of a class of modular Frobenius groups. In fact, we build a connection between modular Frobenius groups and Frobenius–Wielandt groups.

APA, Harvard, Vancouver, ISO, and other styles

38

Guo, Wenbin, and Alexander N. Skiba. "Finite groups with permutable complete Wielandt sets of subgroups." Journal of Group Theory 18, no. 2 (March 1, 2015). http://dx.doi.org/10.1515/jgth-2014-0045.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

MENG, HANGYANG, and XIUYUN GUO. "A NOTE ON WIELANDT’S THEOREM." Bulletin of the Australian Mathematical Society, February 9, 2022, 1–5. http://dx.doi.org/10.1017/s0004972722000120.

Full text

Abstract:

Abstract Let $\pi $ be a set of primes. We say that a group G satisfies $D_{\pi }$ if G possesses a Hall $\pi $ -subgroup H and every $\pi $ -subgroup of G is contained in a conjugate of H. We give a new $D_{\pi }$ -criterion following Wielandt’s idea, which is a generalisation of Wielandt’s and Rusakov’s results.

APA, Harvard, Vancouver, ISO, and other styles

40

Xu, Jing. "Digraph Representations of 2-closed Permutation Groups with a Normal Regular Cyclic Subgroup." Electronic Journal of Combinatorics 22, no. 4 (November 27, 2015). http://dx.doi.org/10.37236/5146.

Full text

Abstract:

In this paper, we classify 2-closed (in Wielandt's sense) permutation groups which contain a normal regular cyclic subgroup and prove that for each such group $G$, there exists a circulant $\Gamma$ such that $\mathrm{Aut} (\Gamma)=G$.

APA, Harvard, Vancouver, ISO, and other styles

41

Xu, Jing, Michael Giudici, Cai Heng Li, and Cheryl E. Praeger. "Invariant Relations and Aschbacher Classes of Finite Linear Groups." Electronic Journal of Combinatorics 18, no. 1 (November 21, 2011). http://dx.doi.org/10.37236/712.

Full text

Abstract:

For a positive integer $k$, a $k$-relation on a set $\Omega$ is a non-empty subset $\Delta$ of the $k$-fold Cartesian product $\Omega^k$; $\Delta$ is called a $k$-relation for a permutation group $H$ on $\Omega$ if $H$ leaves $\Delta$ invariant setwise. The $k$-closure $H^{(k)}$ of $H$, in the sense of Wielandt, is the largest permutation group $K$ on $\Omega$ such that the set of $k$-relations for $K$ is equal to the set of $k$-relations for $H$. We study $k$-relations for finite semi-linear groups $H\leq{\rm\Gamma L}(d,q)$ in their natural action on the set $\Omega$ of non-zero vectors of the underlying vector space. In particular, for each Aschbacher class ${\mathcal C}$ of geometric subgroups of ${\rm\Gamma L}(d,q)$, we define a subset ${\rm Rel}({\mathcal C})$ of $k$-relations (with $k=1$ or $k=2$) and prove (i) that $H$ lies in ${\mathcal C}$ if and only if $H$ leaves invariant at least one relation in ${\rm Rel}({\mathcal C})$, and (ii) that, if $H$ is maximal among subgroups in ${\mathcal C}$, then an element $g\in{\rm\Gamma L}(d,q)$ lies in the $k$-closure of $H$ if and only if $g$ leaves invariant a single $H$-invariant $k$-relation in ${\rm Rel}({\mathcal C})$ (rather than checking that $g$ leaves invariant all $H$-invariant $k$-relations). Consequently both, or neither, of $H$ and $H^{(k)}\cap{\rm\Gamma L}(d,q)$ lie in ${\mathcal C}$. As an application, we improve a 1992 result of Saxl and the fourth author concerning closures of affine primitive permutation groups.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!