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Journal articles on the topic 'Subnormal subgroups'

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Published: 4 June 2021

Last updated: 28 January 2023

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1

Shi, Jiangtao. "Finite groups in which every non-abelian subgroup is a TI-subgroup or a subnormal subgroup." Journal of Algebra and Its Applications 18, no. 08 (July 5, 2019): 1950159. http://dx.doi.org/10.1142/s0219498819501597.

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It is known that a TI-subgroup of a finite group may not be a subnormal subgroup and a subnormal subgroup of a finite group may also not be a TI-subgroup. For the non-abelian subgroups, we prove that if every non-abelian subgroup of a finite group [Formula: see text] is a TI-subgroup or a subnormal subgroup, then every non-abelian subgroup of [Formula: see text] must be subnormal in [Formula: see text]. We also show that the non-cyclic subgroups have the same property.

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2

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.

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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 , .

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3

Kniahina, V. N., and V. S. Monakhov. "Finite groups with semi-subnormal Schmidt subgroups." Algebra and Discrete Mathematics 29, no. 1 (2020): 66–73. http://dx.doi.org/10.12958/adm1376.

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4

Jahan, Iffat, Naseem Ajmal, and Bijan Davvaz. "Subnormality and Theory of L-subgroups." European Journal of Pure and Applied Mathematics 15, no. 4 (October 31, 2022): 2086–115. http://dx.doi.org/10.29020/nybg.ejpam.v15i4.4548.

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The main focus in this work is to establish that L-group theory, which uses the language of functions instead of formal set theoretic language, is capable of capturing most of the refined ideas and concepts of classical group theory. We demonstrate this by extending the notion of subnormality to the L-setting and investigating its properties. We develop a mechanism to tackle the join problem of subnormal L-subgroups. The conjugate L-subgroup as is defined in our previous paper [4] has been used to formulate the concept of normal closure and normal closure series of an L-subgroup which, in turn, is used to define subnormal L-subgroups. Further, the concept of subnormal series has been introduced in L-setting and utilized to establish the subnor-mality of L-subgroups. Also, several results pertaining to the notion of subnormality have been established. Lastly, the level subset characterization of a subnormal L-subgroup is provided after developing a necessary mechanism. Finally, we establish that every subgroup of a nilpotent L-group is subnormal. In fact, it has been exhibited through this work that L-group theory presents a modernized approach to study classical group theory.

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5

Hauck, Peter. "Subnormal subgroups in direct products of groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 42, no. 2 (April 1987): 147–72. http://dx.doi.org/10.1017/s1446788700028172.

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AbstractA group G is called normally (subnormally) detectable if the only normal (subnormal) subgroups in any direct product G1 × … × Gn of copies of G are just the direct factors Gi. We give an internal characterization of finite subnormally detectable groups and obtain analogous results for associative rings and for Lie algebras. The main part of the paper deals with a study of normally detectable groups, where we verify a conjecture of T. O. Hawkes in a number of special cases.

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6

BEIDLEMAN, J. C., and H. HEINEKEN. "GROUPS WITH SUBNORMAL NORMALIZERS OF SUBNORMAL SUBGROUPS." Bulletin of the Australian Mathematical Society 86, no. 1 (February 7, 2012): 11–21. http://dx.doi.org/10.1017/s0004972710032855.

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AbstractWe consider the class of solvable groups in which all subnormal subgroups have subnormal normalizers, a class containing many well-known classes of solvable groups. Groups of this class have Fitting length three at most; some other information connected with the Fitting series is given.

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7

DE FALCO, M., F. DE GIOVANNI, C. MUSELLA, and Y. P. SYSAK. "GROUPS OF INFINITE RANK IN WHICH NORMALITY IS A TRANSITIVE RELATION." Glasgow Mathematical Journal 56, no. 2 (August 30, 2013): 387–93. http://dx.doi.org/10.1017/s0017089513000323.

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AbstractA group is called a T-group if all its subnormal subgroups are normal. It is proved here that if G is a periodic (generalized) soluble group in which all subnormal subgroups of infinite rank are normal, then either G is a T-group or it has finite rank. It follows that if G is an arbitrary group whose Fitting subgroup has infinite rank, then G has the property T if and only if all its subnormal subgroups of infinite rank are normal.

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8

SMITH, HOWARD. "HYPERCENTRAL GROUPS WITH ALL SUBGROUPS SUBNORMAL III." Bulletin of the London Mathematical Society 33, no. 5 (September 2001): 591–98. http://dx.doi.org/10.1112/s0024609301008293.

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It is shown that a hypercentral group that has all subgroups subnormal and every non-nilpotent subgroup of bounded defect is nilpotent. As a consequence, a hypercentral group of length at most ω in which every subgroup is subnormal is nilpotent.

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9

Cossey, John. "Finite groups generated by subnormal T-subgroups." Glasgow Mathematical Journal 37, no. 3 (September 1995): 363–71. http://dx.doi.org/10.1017/s0017089500031645.

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Our aim in this paper is to investigate the restrictions placed on the structure of a finite group if it can be generated by subnormal T-subgroups (a T-group is a group in which every subnormal subgroup is normal). For notational convenience we denote by the class of finite groups that can be generated by subnormal T-subgroups and by the subclass of of those finite groups generated by normal T-subgroups; and for the remainder of this paper we will only consider finite groups.

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10

Monakhov, Victor S., and Irina L. Sokhor. "On groups with formational subnormal Sylow subgroups." Journal of Group Theory 21, no. 2 (March 1, 2018): 273–87. http://dx.doi.org/10.1515/jgth-2017-0039.

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AbstractWe investigate a finite groupGwith{\mathfrak{F}}-subnormal Sylow subgroups, where{\mathfrak{F}}is a subgroup-closed formation and{\mathfrak{A}_{1}\mathfrak{A}\subseteq\mathfrak{F}\subseteq\mathfrak{N}% \mathcal{A}}. We prove thatGis soluble and the derived subgroup of each metanilpotent subgroup is nilpotent. We also describe the structure of groups in which every Sylow subgroup is{\mathfrak{F}}-subnormal or{\mathfrak{F}}-abnormal.

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11

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.

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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.

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12

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.

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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

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13

Maruo, O., and S. E. Stonehewer. "On weakly subnormal subgroups which are not subnormal." Archiv der Mathematik 49, no. 5 (November 1987): 376–78. http://dx.doi.org/10.1007/bf01194093.

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14

OLSHANSKII, A. YU. "Subnormal subgroups in free groups, their growth and cogrowth." Mathematical Proceedings of the Cambridge Philosophical Society 163, no. 3 (February 27, 2017): 499–531. http://dx.doi.org/10.1017/s0305004117000081.

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AbstractIn this paper, the author (1) compare subnormal closures of finite sets in a free group F; (2) obtains the limit for the series of subnormal closures of a single element in F; (3) proves that the exponential growth rate (exp.g.r.) $\lim_{n\to \infty}\sqrt[n]{g_H(n)}$, where gH(n) is the growth function of a subgroup H with respect to a finite free basis of F, exists for any subgroup H of the free group F; (4) gives sharp estimates from below for the exp.g.r. of subnormal subgroups in free groups; and (5) finds the cogrowth of the subnormal closures of free generators.

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15

BALLESTER-BOLINCHES, A., JOHN COSSEY, and X. SOLER-ESCRIVÀ. "ON A PERMUTABILITY PROPERTY OF SUBGROUPS OF FINITE SOLUBLE GROUPS." Communications in Contemporary Mathematics 12, no. 02 (April 2010): 207–21. http://dx.doi.org/10.1142/s0219199710003798.

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The structure and embedding of subgroups permuting with the system normalizers of a finite soluble group are studied in the paper. It is also proved that the class of all finite soluble groups in which every subnormal subgroup permutes with the Sylow subgroups is properly contained in the class of all soluble groups whose subnormal subgroups permute with the system normalizers while this latter is properly contained in the class of all supersoluble groups.

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16

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.

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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.

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17

Kovaleva, Viktoria A. "Finite groups with generalized ℙ-subnormal second maximal subgroups." Asian-European Journal of Mathematics 07, no. 03 (September 2014): 1450047. http://dx.doi.org/10.1142/s1793557114500478.

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A subgroup H of a group G is said to be K-ℙ-subnormal inG [A. F. Vasilyev, T. I. Vasilyeva and V. N. Tyutyanov, On finite groups with almost all K-ℙ-subnormal Sylow subgroups, in Algebra and Combinatorics: Abstracts of Reports of the International Conference on Algebra and Combinatorics on Occasion the 60th Year Anniversary of A. A. Makhnev (Ekaterinburg, 2013), pp. 19–20] if there exists a chain of subgroups H = H0 ≤ H1 ≤ ⋯ ≤ Hn = G such that either Hi-1 is normal in Hi or |Hi : Hi-1| is a prime, for i = 1, …, n. In this paper, we describe finite groups in which every second maximal subgroup is K-ℙ-subnormal.

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18

DE GIOVANNI, FRANCESCO, and MARCO TROMBETTI. "A NOTE ON GROUPS WHOSE PROPER LARGE SUBGROUPS HAVE A TRANSITIVE NORMALITY RELATION." Bulletin of the Australian Mathematical Society 95, no. 1 (November 4, 2016): 38–47. http://dx.doi.org/10.1017/s0004972716000848.

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A group $G$ is said to have the $T$-property (or to be a $T$-group) if all its subnormal subgroups are normal, that is, if normality in $G$ is a transitive relation. The aim of this paper is to investigate the behaviour of uncountable groups of cardinality $\aleph$ whose proper subgroups of cardinality $\aleph$ have a transitive normality relation. It is proved that such a group $G$ is a $T$-group (and all its subgroups have the same property) provided that $G$ has an ascending subnormal series with abelian factors. Moreover, it is shown that if $G$ is an uncountable soluble group of cardinality $\aleph$ whose proper normal subgroups of cardinality $\aleph$ have the $T$-property, then every subnormal subgroup of $G$ has only finitely many conjugates.

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19

Huang, J., B. Hu, and A. N. Skiba. "Finite Groups with Weakly Subnormal and Partially Subnormal Subgroups." Siberian Mathematical Journal 62, no. 1 (January 2021): 169–77. http://dx.doi.org/10.1134/s0037446621010183.

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20

Huang, J., B. Hu, and A. N. Skiba. "Finite groups with weakly subnormal and partially subnormal subgroups." Sibirskii matematicheskii zhurnal 62, no. 1 (February 15, 2021): 210–20. http://dx.doi.org/10.33048/smzh.2021.62.118.

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21

Mason, A. W. "Subnormal subgroups of En(R) have no free, non-abelian quotients, when n≧3." Proceedings of the Edinburgh Mathematical Society 34, no. 1 (February 1991): 113–19. http://dx.doi.org/10.1017/s0013091500005046.

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It is known that for certain rings R (for example R = ℤ, the ring of rational integers) the group GL2(R) contains subnormal subgroups which have free, non-abelian quotients. When such a subgroup has finite index it follows that every countable group is embeddable in a quotient of GL2(R). (In this case GL2(R) is said to be SQ-universal.) In this note we prove that the existence of subnormal subgroups of GL2(R) with this property is a phenomenon peculiar to “n = 2”.For a large class of rings (which includes all commutative rings) it is shown that, for all , no subnormal subgroup of En(R) has a free, non-abelian quotient, when n≧3. (En(R) is the subgroup of GLn(R) generated by the elementary matrices.) In addition it is proved that, if is an SRt-ring, for some t ≧ 2, then no subnormal subgroup of GLn(R) has a free, non-abelian quotient, when n ≧ max (t, 3). From the above these results are best possible since ℤ is an SR3 ring.

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22

Ward, James J. "A Survey of Subnormal Subgroups." Irish Mathematical Society Bulletin 0025 (1990): 38–50. http://dx.doi.org/10.33232/bims.0025.38.50.

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23

Monakhov, Victor, and Irina Sokhor. "On cofactors of subnormal subgroups." Journal of Algebra and Its Applications 15, no. 09 (August 22, 2016): 1650169. http://dx.doi.org/10.1142/s0219498816501693.

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For a soluble finite group [Formula: see text] and a prime [Formula: see text] we let [Formula: see text], [Formula: see text]. We obtain upper bounds for the rank, the nilpotent length, the derived length, and the [Formula: see text]-length of a finite soluble group [Formula: see text] in terms of [Formula: see text] and [Formula: see text].

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24

Detomi, Eloisa. "Groups with many subnormal subgroups." Journal of Algebra 264, no. 2 (June 2003): 385–96. http://dx.doi.org/10.1016/s0021-8693(03)00095-4.

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25

Curzio, Mario. "Some congruences of subnormal subgroups." Rendiconti del Seminario Matematico e Fisico di Milano 65, no. 1 (December 1995): 53–62. http://dx.doi.org/10.1007/bf02925252.

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26

Förster, Peter. "Subnormal subgroups and formation projectors." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 42, no. 1 (February 1987): 31–47. http://dx.doi.org/10.1017/s1446788700033930.

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27

Zarrin, Mohammad. "Non-subnormal subgroups of groups." Journal of Pure and Applied Algebra 217, no. 5 (May 2013): 851–53. http://dx.doi.org/10.1016/j.jpaa.2012.09.006.

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28

Smith, Howard. "Joins of almost subnormal subgroups." Archiv der Mathematik 53, no. 2 (August 1989): 105–9. http://dx.doi.org/10.1007/bf01198558.

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29

Ballester-Bolinches, Adolfo, John Cossey, and Yangming Li. "On a class of finite soluble groups." Journal of Group Theory 21, no. 5 (September 1, 2018): 839–46. http://dx.doi.org/10.1515/jgth-2018-0015.

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Abstract The aim of this paper is to study the class of finite groups in which every subgroup is self-normalising in its subnormal closure. It is proved that this class is a subgroup-closed formation of finite soluble groups which is not closed under taking Frattini extensions and whose members can be characterised by means of their Carter subgroups. This leads to new characterisations of finite soluble T-, PT- and PST-groups. Finite groups whose p-subgroups, p a prime, are self-normalising in their subnormal closure are also characterised.

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30

SMITH, HOWARD. "GROUPS THAT INVOLVE FINITELY MANY PRIMES AND HAVE ALL SUBGROUPS SUBNORMAL II." Glasgow Mathematical Journal 54, no. 3 (March 30, 2012): 529–34. http://dx.doi.org/10.1017/s0017089512000134.

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AbstractIt is shown that if G is a hypercentral group with all subgroups subnormal, and if the torsion subgroup of G is a π-group for some finite set π of primes, then G is nilpotent. In the case where G is not hypercentral there is a section of G that is much like one of the well-known Heineken-Mohamed groups. It is also shown that if G is a residually nilpotent group with all subgroups subnormal whose torsion subgroup satisfies the above condition then G is nilpotent.

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31

CASOLO, CARLO. "NILPOTENT SUBGROUPS OF GROUPS WITH ALL SUBGROUPS SUBNORMAL." Bulletin of the London Mathematical Society 35, no. 01 (January 2003): 15–22. http://dx.doi.org/10.1112/s0024609302001443.

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32

BALLESTER-BOLINCHES, A., J. C. BEIDLEMAN, A. D. FELDMAN, and M. F. RAGLAND. "ON GENERALISED PRONORMAL SUBGROUPS OF FINITE GROUPS." Glasgow Mathematical Journal 56, no. 3 (August 22, 2014): 691–703. http://dx.doi.org/10.1017/s0017089514000159.

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AbstractFor a formation $\mathfrak F$, a subgroup M of a finite group G is said to be $\mathfrak F$-pronormal in G if for each g ∈ G, there exists x ∈ 〈U,Ug〉$\mathfrak F$ such that Ux = Ug. Let f be a subgroup embedding functor such that f(G) contains the set of normal subgroups of G and is contained in the set of Sylow-permutable subgroups of G for every finite group G. Given such an f, let fT denote the class of finite groups in which f(G) is the set of subnormal subgroups of G; this is the class of all finite groups G in which to be in f(G) is a transitive relation in G. A subgroup M of a finite group G is said to be $\mathfrak F$-normal in G if G/CoreG(M) belongs to $\mathfrak F$. A subgroup U of a finite group G is called K-$\mathfrak F$-subnormal in G if either U = G or there exist subgroups U = U0 ≤ U1 ≤ . . . ≤ Un = G such that Ui–1 is either normal or $\mathfrak F$-normal in Ui, for i = 1,2, …, n. We call a finite group G an $fT_{\mathfrak F}$-group if every K-$\mathfrak F$-subnormal subgroup of G is in f(G). In this paper, we analyse for certain formations $\mathfrak F$ the structure of $fT_{\mathfrak F}$-groups. We pay special attention to the $\mathfrak F$-pronormal subgroups in this analysis.

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33

Semenchuk, Vladimir N., and Alexander N. Skiba. "On one generalization of finite 𝔘-critical groups." Journal of Algebra and Its Applications 15, no. 04 (February 19, 2016): 1650063. http://dx.doi.org/10.1142/s0219498816500638.

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A proper subgroup [Formula: see text] of a group [Formula: see text] is said to be: [Formula: see text]-subnormal in [Formula: see text] if there exists a chain of subgroups [Formula: see text] such that [Formula: see text] is a prime for [Formula: see text]; [Formula: see text]-abnormal in [Formula: see text] if for every two subgroups [Formula: see text] of [Formula: see text], where [Formula: see text], [Formula: see text] is not a prime. In this paper we describe finite groups in which every non-identity subgroup is either [Formula: see text]-subnormal or [Formula: see text]-abnormal.

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34

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.

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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.

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35

Kurdachenko, L. A., and N. N. Semko. "On the structure of some groups having finite contranormal subgroups." Algebra and Discrete Mathematics 31, no. 1 (2021): 109–19. http://dx.doi.org/10.12958/adm1724.

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Following J.S. Rose, a subgroup H of the group G is said to be contranormal in G, if G=HG. In a certain sense, contranormal subgroups are antipodes to subnormal subgroups. We study the structure of Abelian-by-nilpotent groups having a finite proper contranormal p-subgroup.

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36

Hai, Bui Xuan, and Nguyen Anh Tu. "On multiplicative subgroups in division rings." Journal of Algebra and Its Applications 15, no. 03 (January 27, 2016): 1650050. http://dx.doi.org/10.1142/s021949881650050x.

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Let [Formula: see text] be a division ring. In this paper, we investigate properties of subgroups of an arbitrary subnormal subgroup of the multiplicative group [Formula: see text] of [Formula: see text]. The new obtained results generalize some previous results on subgroups of [Formula: see text].

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37

Guralnick, Robert, Peter B. Kleidman, and Richard Lyons. "Sylow p -Subgroups and Subnormal Subgroups of Finite Groups." Proceedings of the London Mathematical Society s3-66, no. 1 (January 1993): 129–51. http://dx.doi.org/10.1112/plms/s3-66.1.129.

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38

Ballester-Bolinches, A., J. C. Beidleman, and H. Heineken. "Groups in which Sylow subgroups and subnormal subgroups permute." Illinois Journal of Mathematics 47, no. 1-2 (March 2003): 63–69. http://dx.doi.org/10.1215/ijm/1258488138.

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39

Hassanzadeh, Mahmoud, and Zohreh Mostaghim. "On groups whose self-centralizing subgroups are normal." Journal of Algebra and Its Applications 18, no. 06 (May 27, 2019): 1950106. http://dx.doi.org/10.1142/s0219498819501068.

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In this paper, we prove that a group is nilpotent of class at most two if and only if each of its self-centralizing subgroups is normal. We also show that if all self-centralizing subgroups of a certain group are subnormal then all subgroups are subnormal.

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40

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.

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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).

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41

Goncalves, Jairo, Jurgen Ritter, and Sudarshan Sehgal. "Subnormal Subgroups in U( Z G)." Proceedings of the American Mathematical Society 103, no. 2 (June 1988): 375. http://dx.doi.org/10.2307/2047144.

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42

Casolo, Carlo. "On Groups with all Subgroups Subnormal." Bulletin of the London Mathematical Society 17, no. 4 (July 1985): 397. http://dx.doi.org/10.1112/blms/17.4.397.

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43

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.

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Kegel, O. H. "Book Review: Subnormal subgroups of groups." Bulletin of the American Mathematical Society 21, no. 2 (October 1, 1989): 346–48. http://dx.doi.org/10.1090/s0273-0979-1989-15855-2.

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Marciniak, Zbigniew S., and Sudarshan K. Sehgal. "Subnormal subgroups of group ring units." Proceedings of the American Mathematical Society 126, no. 2 (1998): 343–48. http://dx.doi.org/10.1090/s0002-9939-98-04126-4.

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Tazhetdinov, S. "On subnormal subgroups of linear groups." Siberian Mathematical Journal 49, no. 1 (January 2008): 175–79. http://dx.doi.org/10.1007/s11202-008-0018-8.

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Makar-Limanov, L. "On subnormal subgroups of skew fields." Journal of Algebra 114, no. 2 (May 1988): 261–67. http://dx.doi.org/10.1016/0021-8693(88)90295-5.

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Knyagina, V. N., and V. S. Monakhov. "Finite Groups with Subnormal Schmidt Subgroups." Siberian Mathematical Journal 45, no. 6 (November 2004): 1075–79. http://dx.doi.org/10.1023/b:simj.0000048922.59466.20.

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Franciosi, Silvana, Francesco de Giovanni, and Yaroslav P. Sysak. "On Subnormal Subgroups of Factorized Groups." Journal of Algebra 198, no. 2 (December 1997): 469–80. http://dx.doi.org/10.1006/jabr.1997.7150.

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Ballester-Bolinches, A., J. C. Beidleman, John Cossey, R. Esteban-Romero, M. F. Ragland, and Jack Schmidt. "Permutable subnormal subgroups of finite groups." Archiv der Mathematik 92, no. 6 (May 12, 2009): 549–57. http://dx.doi.org/10.1007/s00013-009-2976-x.

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