Results 21 to 30 of about 94 (79)
Gruenberg-Kegel graphs: cut groups, rational groups and the Prime Graph Question
, 2022 The Gruenberg-Kegel graph of a group is the undirected graph whose vertices are those primes which occur as the order of an element of the group, and distinct vertices $p$, $q$ are joined by an edge whenever the group has an element of order $pq$.
Maheshwary, Sugandha +3 more
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A note on finite group structure influenced by second and third maximal subgroups
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 4, Page 747-750, 1990., 1990 The structure of a finite group having specified number of second and third maximal subgroups has been investigated in the paper.
N. P. Mukherjee, R. Khazal
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
Generating fast Fourier transforms of solvable groups
, 2003 This paper presents a new algorithm for constructing a complete list of pairwise inequivalent ordinary irreducible representations of a finite solvable group G.
Clausen, M. +3 more
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On stabilizers in finite permutation groups
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract Let G$G$ be a permutation group on the finite set Ω$\Omega$. We prove various results about partitions of Ω$\Omega$ whose stabilizers have good properties. In particular, in every solvable permutation group there is a set‐stabilizer whose orbits have length at most 6, which is best possible and answers two questions of Babai.
Luca Sabatini
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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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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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Groups with hypercyclic proper quotient groups
, 2003 We continue the investigation of (solvable) groups all proper subgroups of which are hypercyclic. The monolithic case is studied completely; in the nonmonolithic case, however, one should impose certain additional conditions.
Soules, P., Kurdachenko, L.A.
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System quasinormalizers in finite solvable groups
, 1977 Let ∑ denote a Sylow system of the finite solvable group G. The system quasinormalizer of G, associated with ∑, is the subgroup of G generated by all elements x such that 〈x〉 permutes with each element of ∑.
Venzke, Paul
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