Results 41 to 50 of about 1,123 (134)
A generalized Frattini subgroup of a finite group
International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 2, Page 263-266, 1989., 1989 For a finite group G and an arbitrary prime p, let SP(G) denote the intersection of all maximal subgroups M of G such that [G:M] is both composite and not divisible by p; if no such M exists we set SP(G) = G. Some properties of G are considered involving SP(G).
Prabir Bhattacharya, N. P. Mukherjee
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On the number of cyclic subgroups of a finite group
, 2018 Let $G$ be a finite group and let $c(G)$ be the number of cyclic subgroups of $G$. We study the function $\alpha(G) = c(G)/|G|$. We explore its basic properties and we point out a connection with the probability of commutation.
Garonzi, Martino, Lima, Igor
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A Jordan–Chevalley decomposition beyond algebraic groups
Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.Abstract We prove a decomposition of definable groups in o‐minimal structures generalizing the Jordan–Chevalley decomposition of linear algebraic groups. It follows that any definable linear group G$G$ is a semidirect product of its maximal normal definable torsion‐free subgroup N(G)$\mathcal {N}(G)$ and a definable subgroup P$P$, unique up to ...
Annalisa Conversano
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A note on influence of subgroup restrictions in finite group structure
International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 4, Page 721-724, 1989., 1988 The structure of a finite group under specific restrictions respectively on its maximal, minimal and prime power subgroups has been investigated in this paper.
R. Khazal, N. P. Mukherjee
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Approximate groups and doubling metrics
, 2012 We develop a version of Freiman's theorem for a class of non-abelian groups, which includes finite nilpotent, supersolvable and solvable A-groups. To do this we have to replace the small doubling hypothesis with a stronger relative polynomial growth ...
Bray +7 more
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Bulletin of the London Mathematical Society, Volume 56, Issue 3, Page 1054-1070, March 2024.Abstract Let d$d$ be a positive integer. A finite group is called d$d$‐maximal if it can be generated by precisely d$d$ elements, whereas its proper subgroups have smaller generating sets. For d∈{1,2}$d\in \lbrace 1,2\rbrace$, the d$d$‐maximal groups have been classified up to isomorphism and only partial results have been proved for larger d$d$.
Andrea Lucchini +2 more
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The first Hochschild cohomology as a Lie algebra
, 2019 In this paper we study sufficient conditions for the solvability of the first Hochschild cohomology of a finite dimensional algebra as a Lie algebra in terms of its Ext-quiver in arbitrary characteristic.
Degrassi, Lleonard Rubio y +2 more
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Inductive and divisional posets
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract We call a poset factorable if its characteristic polynomial has all positive integer roots. Inspired by inductive and divisional freeness of a central hyperplane arrangement, we introduce and study the notion of inductive posets and their superclass of divisional posets.
Roberto Pagaria +3 more
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Известия Иркутского государственного университета: Серия "Математика"The concept of $X$-permutable subgroup, introduced by A. N. Skiba, generalizes the classical concept of a permutable subgroup. Many classes of finite groups have been characterized in terms of $X$-permutable subgroups.
A. A. Galt, V. N. Tyutyanov
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Finite group with some c#-normal and S-quasinormally embedded subgroups
Open MathematicsLet pp be a prime that divides the order of a finite group GG, and let PP be a Sylow pp-subgroup of GG. Assume that dd is the smallest number of generators of PP and define ℳd(P)={P1,P2,…,Pd}{{\mathcal{ {\mathcal M} }}}_{d}\left(P)=\left\{{P}_{1},{P}_{2},
Li Ning, Jiang Jing, Liu Jianjun
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