Results 1 to 10 of about 75,062 (163)
Finite Groups Isospectral to Simple Groups
Communications in Mathematics and Statistics, 2022 The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum, in particular, to list all finite simple groups for which the recognition problem is solved.
Maria A Grechkoseeva +2 more
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Non-simple localizations of finite simple groups
Journal of Algebra, 2006 10 ...
Jérôme Scherer +2 more
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A Characterization of the Finite Simple Groups
Journal of Algebra, 2001 The first main theorem is that if \(N\) and \(G\) are simple groups with \(|N|\) dividing \(|G|\), all indices of maximal subgroups of \(N\) being indices of maximal subgroups of \(G\), and the smallest such index being equal to the two groups, then \(N=G\) except in the two cases \((N,G)=(L_2(11),M_{11})\) and \((N,G)=(U_3(3),S_6(2))\). The proof uses
exaly +2 more sources
Infinite locally finite simple groups with many complemented subgroups [PDF]
International Journal of Group Theory, 2022 We prove that the following families of (infinite) groups have complemented subgroup lattice: alternating groups, finitary symmetric groups, Suzuki groups over an infinite locally finite field of characteristic $2$, Ree groups over an infinite ...
Maria Ferrara, Marco Trombetti
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Characterization of some alternating groups by order and largest element order [PDF]
AUT Journal of Mathematics and Computing, 2022 The prime graph (or Gruenberg-Kegel graph) of a finite group is a well-known graph. In this paper, first, we investigate the structure of the finite groups with a non-complete prime graph.
Ali Mahmoudifar, Ayoub Gharibkhajeh
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The minimum sum of element orders of finite groups [PDF]
International Journal of Group Theory, 2021 Let $ G $ be a finite group and \( \psi(G)=\sum_{g\in G}o(g) \), where $ o(g) $ denotes the order of $g\in G$. We show that the Conjecture 4.6.5 posed in [Group Theory and Computation, (2018) 59-90], is incorrect.
Maghsoud Jahani +3 more
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A new characterization of some characteristically simple groups [PDF]
AUT Journal of Mathematics and Computing, 2023 Let $G$ be a finite group and $\mathrm{cd}(G)$ be the set of irreducible complex character degrees of $G$. It was proved that some finite simple groups are uniquely determined by their orders and their degree graphs.
Zohreh Sayanjali
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On conjugacy classes of the F4 group over a field q with characteristic 2
St. Petersburg Polytechnical University Journal: Physics and Mathematics, 2022 This article continues a series of papers devoted to solving the problem by which a non-identity conjugacy class in a finite simple non-abelian group contains commuting elements. Previously, this statement was tested for sporadic, projective, alternating
Yurova Nadezhda
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Finite groups with the same conjugacy class sizes as a finite simple group [PDF]
International Journal of Group Theory, 2019 For a finite group $H$, let $cs(H)$ denote the set of non-trivial conjugacy class sizes of $H$ and $OC(H)$ be the set of the order components of $H$. In this paper, we show that if $S$ is a finite simple group with the disconnected prime graph and $
Neda Ahanjideh
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On recognizing groups by the bottom layer [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 The article discusses the possibility of recognizing a group by the bottom layer, that is, by the set of its elements of prime orders. The paper gives examples of groups recognizable by the bottom layer, almost recognizable by the bottom layer, and ...
V.I. Senashov, I.A. Paraschuk
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