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Articles de revues sur le sujet « Π-separable groups »

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Auteur : Grafiati
Publié le 10 mars 2023

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1

Berkovich, Yakov. « On π-Separable Groups ». Journal of Algebra 186, no 1 (novembre 1996) : 120–31. http://dx.doi.org/10.1006/jabr.1996.0366.

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2

Laradji, A. « Relative π-Blocks of π-Separable Groups ». Journal of Algebra 220, no 2 (octobre 1999) : 449–65. http://dx.doi.org/10.1006/jabr.1999.7945.

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3

Laradji, A. « Relative π-Blocks of π-Separable Groups, II ». Journal of Algebra 237, no 2 (mars 2001) : 521–32. http://dx.doi.org/10.1006/jabr.2000.8575.

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4

Si, Huabin, et Jiwen Zeng. « The Character Correspondences on π-Separable Groups ». Algebra Colloquium 19, no 03 (5 juillet 2012) : 501–8. http://dx.doi.org/10.1142/s1005386712000363.

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In this paper, we mainly consider the relationship between the complex irreducible characters of a π-separable group and the complex irreducible characters of its Hall π-subgroup. If a π-group S acts on a π-separable group G, let H be an S-invariant Hall π-subgroup of G and CNG(H)/H(S)=1. Then we construct a natural bijection from the set Lin S(H) onto the set Irr π′,S(G). Furthermore, we get a bijection from the linear characters of H onto Irr π′(G).
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5

Iranzo, M. J., F. Pérez Monasor et J. Medina. « ARITHMETICAL QUESTIONS IN π-SEPARABLE GROUPS ». Communications in Algebra 33, no 8 (juillet 2005) : 2713–16. http://dx.doi.org/10.1081/agb-200063998.

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6

Du, Zhaowei. « Hall Subgroups and π-Separable Groups ». Journal of Algebra 195, no 2 (septembre 1997) : 501–9. http://dx.doi.org/10.1006/jabr.1997.7034.

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7

Isaacs, I. M. « Fong characters in π-separable groups ». Journal of Algebra 99, no 1 (mars 1986) : 89–107. http://dx.doi.org/10.1016/0021-8693(86)90056-6.

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8

Wolf, Thomas R. « Character Correspondences and π-Special Characters in π-Separable Groups ». Canadian Journal of Mathematics 39, no 4 (1 août 1987) : 920–37. http://dx.doi.org/10.4153/cjm-1987-046-1.

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Let π be a set of primes and let G be a π-separable group (all groups considered are finite). Two subsets Xπ(G) and Bπ(G) of the set Irr(G) of irreducible characters of G play an important role in the character theory of π-separable groups and particularly solvable groups. If p is prime and π is the set of all other primes, then the Bπ characters of G give a natural one-to-one lift of the Brauer characters of G into Irr(G). More generally, they have been used to define Brauer characters for sets of primes.The π-special characters of G (i.e., Xπ(G)) restrict irreducibly and in a one-to-one fashion to a Hall-π-subgroup of G. If an irreducible character χ is quasi-primitive, it factors uniquely as a product of a π-special character an a π′-special character. This is a particularly useful tool in solvable groups.
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9

Grittini, Nicola. « Character degrees in 𝜋-separable groups ». Journal of Group Theory 23, no 6 (1 novembre 2020) : 1069–80. http://dx.doi.org/10.1515/jgth-2019-0186.

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AbstractIf a group G is π-separable, where π is a set of primes, the set of irreducible characters {\operatorname{B}_{\pi}(G)\cup\operatorname{B}_{\pi^{\prime}}(G)} can be defined. In this paper, we prove variants of some classical theorems in character theory, namely the theorem of Ito–Michler and Thompson’s theorem on character degrees, involving irreducible characters in the set {\operatorname{B}_{\pi}(G)\cup\operatorname{B}_{\pi^{\prime}}(G)}.
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10

Isaacs, I. M. « Extensions of characters from Hall π-subgroups of π-separable groups ». Proceedings of the Edinburgh Mathematical Society 28, no 3 (octobre 1985) : 313–17. http://dx.doi.org/10.1017/s0013091500017120.

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The main result of this paper is the followingTheorem A. Let G be a π-separable finite group with Hall πsubgroup H. Suppose θεIrr(H). Then there exists a unique subgroup M, maximal with the property that it contains H and θ can be extended to a character of M.
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11

Robinson, Geoffrey R., et Reiner Staszewski. « On the representation theory of π-separable groups ». Journal of Algebra 119, no 1 (novembre 1988) : 226–32. http://dx.doi.org/10.1016/0021-8693(88)90086-5.

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12

Navarro, Gabriel. « Fong Characters and Correspondences in π-Separable Groups ». Canadian Journal of Mathematics 43, no 2 (1 avril 1991) : 405–12. http://dx.doi.org/10.4153/cjm-1991-023-9.

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Let G and S be finite groups. Suppose that S acts on G with (|G|, |S| ) = 1. If S is solvable, Glauberman showed the existence of a natural bijection from lrrs(G) = ﹛ χ ∈ Irr(G) | χs = χ for a11 s ∈ S﹜ on to Irr(C), where C = CG(S). If S is not solvable, and consequently | G| is odd, Isaacs also proved the existence of a natural bijection between the above set of characters. Finally, Wolf proved that both maps agreed when both were defined ([1], [3], [10]). As in [7], let us denote by *: Irrs(G) → Irr(C) the Glauberman-Isaacs Correspondence.
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13

KISHIMOTO, AKITAKA. « APPROXIMATELY INNER FLOWS ON SEPARABLE C*-ALGEBRAS ». Reviews in Mathematical Physics 14, no 07n08 (juillet 2002) : 649–73. http://dx.doi.org/10.1142/s0129055x02001284.

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We present two types of result for approximately inner one-parameter automorphism groups (referred to as AI flows hereafter) of separable C*-algebras. First, if there is an irreducible representation π of a separable C*-algebra A such that π(A) does not contain non-zero compact operators, then there is an AI flow α such that π is α-covariant and α is far from uniformly continuous in the sense that α induces a flow on π(A) which has full Connes spectrum. Second, if α is an AI flow on a separable C*-algebra A and π is an α-covariant irreducible representation, then we can choose a sequence (hn) of self-adjoint elements in A such that αt is the limit of inner flows Ad eithn and the sequence π(eithn) of one-parameter unitary groups (referred to as unitary flows hereafter) converges to a unitary flow which implements α in π. This latter result will be extended to cover the case of weakly inner type I representations. In passing we shall also show that if two representations of a separable simple C*-algebra on a separable Hilbert space generate the same von Neumann algebra of type I, then there is an approximately inner automorphism which sends one into the other up to equivalence.
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14

Poimenidou, Eirini. « Fong characters and normal subgroups of π-separable groups ». Journal of Algebra 151, no 1 (septembre 1992) : 192–217. http://dx.doi.org/10.1016/0021-8693(92)90139-d.

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15

Isaacs, I. M., et G. Navarro. « Weights and Vertices for Characters of π-Separable Groups ». Journal of Algebra 177, no 2 (octobre 1995) : 339–66. http://dx.doi.org/10.1006/jabr.1995.1301.

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16

Sanus, Lucía. « Blocks Relative to a Normal Subgroup in π-Separable Groups ». Journal of Algebra 232, no 1 (octobre 2000) : 343–59. http://dx.doi.org/10.1006/jabr.1999.8410.

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17

Sambale, Benjamin. « Solution of Brauer’s k ⁢ ( B ) k(B) -conjecture for π-blocks of π-separable groups ». Forum Mathematicum 30, no 4 (1 juillet 2018) : 1061–64. http://dx.doi.org/10.1515/forum-2017-0147.

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Abstract Answering a question of Pálfy and Pyber, we first prove the following extension of the {k(GV)} -problem: Let G be a finite group and let A be a coprime automorphism group of G. Then the number of conjugacy classes of the semidirect product {G\rtimes A} is at most {\lvert G\rvert} . As a consequence, we verify Brauer’s {k(B)} -conjecture for π-blocks of π-separable groups which was proposed by Y. Liu. This generalizes the corresponding result for blocks of p-solvable groups. We also discuss equality in Brauer’s Conjecture. On the other hand, we construct a counterexample to a version of Olsson’s Conjecture for π-blocks which was also introduced by Liu.
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18

Abdelmoula, Lobna, Ali Baklouti et Yasmine Bouaziz. « On the generalized moment separability theorem for type 1 solvable Lie groups ». Advances in Pure and Applied Mathematics 9, no 4 (1 octobre 2018) : 247–77. http://dx.doi.org/10.1515/apam-2018-0020.

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Abstract Let G be a type 1 connected and simply connected solvable Lie group. The generalized moment map for π in {\widehat{G}} , the unitary dual of G, sends smooth vectors of the representation space of π to {{\mathcal{U}(\mathfrak{g})}^{*}} , the dual vector space of {\mathcal{U}(\mathfrak{g})} . The convex hull of the image of the generalized moment map for π is called its generalized moment set, denoted by {J(\pi)} . We say that {\widehat{G}} is generalized moment separable when the generalized moment sets differ for any pair of distinct irreducible unitary representations. Our main result in this paper provides a second proof of the generalized moment separability theorem for G.
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19

Liu, Qin Tao, et Jin Ke Hai. « On the Monomial Bπ-Character of a Finite π-Separable Group ». Applied Mechanics and Materials 475-476 (décembre 2013) : 1071–74. http://dx.doi.org/10.4028/www.scientific.net/amm.475-476.1071.

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Let π be a set of primes. Isaacs established the π-theory of characters, which generalizes the theory of Brauer module characters. Based on Isaacss work, we introduce the definition of Mπ-groups, and prove that if G=NwrCp is an Mπ-group, where Cp is a cyclic group of order p and pπ, then N is an Mπ-group.
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20

Filali, M., et M. Sangani Monfared. « A Cohomological Property of π-invariant Elements ». Canadian Mathematical Bulletin 56, no 3 (1 septembre 2013) : 534–43. http://dx.doi.org/10.4153/cmb-2011-184-7.

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Abstract.Let A be a Banach algebra and let be a continuous representation of A on a separable Hilbert space H with dim H = m. Let πi j be the coordinate functions of π with respect to an orthonormal basis and suppose that for each and . Under these conditions, we call an element left π-invariant if In this paper we prove a link between the existence of left π-invariant elements and the vanishing of certain Hochschild cohomology groups of A. Our results extend an earlier result by Lau on F-algebras and recent results of Kaniuth, Lau, Pym, and and the second author in the special case where π : A → C is a non-zero character on A.
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21

Ando, Hiroshi, Yasumichi Matsuzawa, Andreas Thom et Asger Törnquist. « Unitarizability, Maurey–Nikishin factorization, and Polish groups of finite type ». Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no 758 (1 janvier 2020) : 223–51. http://dx.doi.org/10.1515/crelle-2017-0047.

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AbstractLet Γ be a countable discrete group, and let {\pi\colon\Gamma\to{\rm{GL}}(H)} be a representation of Γ by invertible operators on a separable Hilbert space H. We show that the semidirect product group {G=H\rtimes_{\pi}\Gamma} is SIN (G admits a two-sided invariant metric compatible with its topology) and unitarily representable (G embeds into the unitary group {\mathcal{U}(\ell^{2}(\mathbb{N}))}) if and only if π is uniformly bounded, and that π is unitarizable if and only if G is of finite type, that is, G embeds into the unitary group of a {\mathrm{II}_{1}}-factor. Consequently, we show that a unitarily representable Polish SIN group need not be of finite type, answering a question of Sorin Popa. The key point in our argument is an equivariant version of the Maurey–Nikishin factorization theorem for continuous maps from a Hilbert space to the space {L^{0}(X,m)} of all measurable maps on a probability space.
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22

Lewis, Mark L. « Nuclei and Lifts of π-Partial Characters ». Algebra Colloquium 16, no 01 (mars 2009) : 167–80. http://dx.doi.org/10.1142/s1005386709000182.

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In this paper, we obtain a common generalization of the Isaacs and Navarro constructions of nuclei for characters of π-separable groups. The construction of Isaacs used the lattice of all subnormal subgroups, and the construction of Navarro used the lattice of all normal subgroups. We show that a generalized nucleus can be constructed using other lattices of subnormal subgroups, and these nuclei have properties similar to the properties of the nuclei constructed by Isaacs and Navarro.
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23

Isaacs, I. M. « Coprime Group Actions Fixing All Nonlinear Irreducible Characters ». Canadian Journal of Mathematics 41, no 1 (1 février 1989) : 68–82. http://dx.doi.org/10.4153/cjm-1989-003-2.

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The main result of this paper is the following:Theorem A. Let H and N be finite groups with coprime orders andsuppose that H acts nontrivially on N via automorphisms. Assume that Hfixes every nonlinear irreducible character of N. Then the derived subgroup ofN is nilpotent and so N is solvable of nilpotent length≦ 2.Why might one be interested in a situation like this? There has been considerable interest in the question of what one can deduce about a group Gfrom a knowledge of the setcd(G) = ﹛x(l)lx ∈ Irr(G) ﹜of irreducible character degrees of G.Recently, attention has been focused on the prime divisors of the elements of cd(G). For instance, in [9], O. Manz and R. Staszewski consider π-separable groups (for some set π of primes) with the property that every element of cd(G) is either a 77-number or a π'-number.
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24

Isaacs, I. M. « Induction and Restriction of π-Special Characters ». Canadian Journal of Mathematics 38, no 3 (1 juin 1986) : 576–604. http://dx.doi.org/10.4153/cjm-1986-029-5.

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1. Introduction. The character theory of solvable groups has undergone significant development during the last decade or so and it can now be seen to have quite a rich structure. In particular, there is an interesting interaction between characters and sets of prime numbers.Let G be solvable and let π be a set of primes. The “π-special” characters of G are certain irreducible complex characters (defined by D. Gajendragadkar [1]) which enjoy some remarkable properties, many of which were proved in [1]. (We shall review the definition and relevant facts in Section 3 of this paper.) Actually, we need not assume solvability: that G is π-separable is sufficient, if we are willing to use the Feit-Thompson “odd order” theorem occasionally. We shall state and prove our results under this weaker hypothesis, but we stress that anything of interest in them is already interesting in the solvable case where, of course, the “odd order” theorem is irrelevant.
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25

Isaacs, I. M. « Induction and Restriction of π-Partial Characters and their Lifts ». Canadian Journal of Mathematics 48, no 6 (1 décembre 1996) : 1210–23. http://dx.doi.org/10.4153/cjm-1996-064-9.

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AbstractLet G be a finite π-separable group, where π is a set of primes. The π-partial characters of G are the restrictions of the ordinary characters to the set of π-elements of G. Such an object is said to be irreducible if it is not the sum of two nonzero partial characters and the set of irreducible π- partial characters of G is denoted Iπ(G). (If p is a prime and π = p′, then Iπ(G) is exactly the set of irreducible Brauer characters at p.)From their definition, it is obvious that each partial character φ ∊ Iπ(G) can be “lifted” to an ordinary character χ ∊ Irr(G). (This means that φ is the restriction of χ to the π-elements of G.) In fact, there is a known set of canonical lifts Bπ(G) ⊆ Irr(G) for the irreducible π-partial characters. In this paper, it is proved that if 2 ∉ π, then there is an alternative set of canonical lifts (denoted Dπ(G)) that behaves better with respect to character induction.An application of this theory to M-groups is presented. If G is an M-group and S ⊆ G is a subnormal subgroup, consider a primitive character θ ⊆ Irr(S). It was known previously that if |G : S| is odd, then θ must be linear. It is proved here without restriction on the index of S that θ(1) is a power of 2.
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26

Arroyo-Jordá, Milagros, Paz Arroyo-Jordá, Rex Dark, Arnold D. Feldman et María Dolores Pérez-Ramos. « Carter and Gaschütz theories beyond soluble groups ». Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 116, no 2 (11 février 2022). http://dx.doi.org/10.1007/s13398-022-01215-7.

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AbstractClassical results from the theory of finite soluble groups state that Carter subgroups, i.e. self-normalizing nilpotent subgroups, coincide with nilpotent projectors and with nilpotent covering subgroups, and they form a non-empty conjugacy class of subgroups, in soluble groups. This paper presents an extension of these facts to $$\pi $$ π -separable groups, for sets of primes $$\pi $$ π , by proving the existence of a conjugacy class of subgroups in $$\pi $$ π -separable groups, which specialize to Carter subgroups within the universe of soluble groups. The approach runs parallel to the extension of Hall theory from soluble to $$\pi $$ π -separable groups by Čunihin, regarding existence and properties of Hall subgroups.
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27

Журтов, А. Х., et З. Б. Селяева. « On locally finite π-separable groups ». Владикавказский математический журнал, no 2 (5 juin 2015). http://dx.doi.org/10.23671/vnc.2015.2.7273.

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28

Arroyo-Jordá, M., P. Arroyo-Jordá, R. Dark, A. D. Feldman et M. D. Pérez-Ramos. « Injectors in $$\pi $$-Separable Groups ». Mediterranean Journal of Mathematics 19, no 4 (24 juin 2022). http://dx.doi.org/10.1007/s00009-022-02079-2.

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AbstractLet $$\pi $$ π be a set of primes. We show that $$\pi $$ π -separable groups have a conjugacy class of $${\mathfrak {F}}$$ F -injectors for suitable Fitting classes $${\mathfrak {F}}$$ F , which coincide with the usual ones when specializing to soluble groups.
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29

Wang, Lei, et Ping Jin. « The uniqueness of vertex pairs in π-separable groups ». Communications in Algebra, 15 février 2023, 1–6. http://dx.doi.org/10.1080/00927872.2023.2177045.

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