Results 11 to 20 of about 998,375 (277)
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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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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Finite simple groups as expanders [PDF]
Proceedings of the National Academy of Sciences, 2006 We prove that there exist k ∈ ℕ and 0 < ε ∈ ℝ such that every non-abelian finite simple group G , which is not a Suzuki group, has a set of k generators for which the Cayley graph Cay( G ; S ) is an ε-expander.
Kassabov, M, Lubotzky, A, Nikolov, N
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The reduction theorem for relatively maximal subgroups
Bulletin of Mathematical Sciences, 2022 Let [Formula: see text] be a class of finite groups closed under taking subgroups, homomorphic images and extensions. It is known that if [Formula: see text] is a normal subgroup of a finite group [Formula: see text] then the image of an [Formula: see ...
Wenbin Guo +2 more
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The recognition of finite simple groups with no elements of order $10$ by their element orders [PDF]
International Journal of Group Theory, 2022 The spectrum of a finite group is the set of its element orders. $H$ is said to be a finite cover of $G$ if $G$ is a homomorphic image of $H$ and $H$ is finite.
Huaiyu He, Wujie Shi
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$4$-Regular prime graphs of nonsolvable groups [PDF]
International Journal of Group Theory, 2020 Let $G$ be a finite group and $\cd(G)$ denote the character degree set for $G$. The prime graph $\DG$ is a simple graph whose vertex set consists of prime divisors of elements in $\cd(G)$, denoted $\rho(G)$.
Donnie Kasyoki, Paul Oleche
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Divisibility and laws in finite simple groups [PDF]
Mathematische Annalen, 2015 20 pages, no figures; v3 completely rewritten with new co-author and new ...
Gady Kozma, Andreas Thom
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On two generation methods for the simple linear group $PSL(3,7)$ [PDF]
AUT Journal of Mathematics and Computing, 2023 A finite group $G$ is said to be \textit{$(l,m, n)$-generated}, if it is a quotient group of the triangle group $T(l,m, n) = \left.$ In [J. Moori, $(p, q, r)$-generations for the Janko groups $J_{1}$ and $J_{2}$, Nova J.
Thekiso Seretlo
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Products of squares in finite simple groups [PDF]
Proceedings of the American Mathematical Society, 2011 The Ore conjecture, proved by the authors, states that every element of every finite non-abelian simple group is a commutator. In this paper we use similar methods to prove that every element of every finite simple group is a product of two squares. This can be viewed as a non-commutative analogue of Lagrange’s four squares theorem.
Liebeck, Martin W. +3 more
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Equal-Square Graphs Associated with Finite Groups
Journal of Mathematics, 2022 The graphical representation of finite groups is studied in this paper. For each finite group, a simple graph is associated for which the vertex set contains elements of group such that two distinct vertices x and y are adjacent iff x2=y2.
Shafiq Ur Rehman +3 more
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