Results 11 to 20 of about 52,060 (313)
On a New Criterion for the Solvability of Non-Simple Finite Groups and m-Abelian Solvability [PDF]
Journal of Mathematics, 2021 This paper is devoted to introduce a sufficient condition for the solvability of finite groups. Also, it presents the concepts of m-abelian and m-cyclic solvability as new generalizations of solvability and polycyclicity, respectively.
Hasan Sankari, Mohammad Abobala
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Finite simple groups as expanders. [PDF]
Proc Natl Acad Sci U S A, 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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Infinite products of finite simple groups [PDF]
Transactions of the American Mathematical Society, 1996 We classify the sequences ⟨ S n ∣ n ∈ N ⟩ \langle S_{n} \mid n \in \mathbb {N} \rangle of finite simple nonabelian groups such that ∏ n S
Jan Saxl, Saharon Shelah, Simon Thomas
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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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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 +4 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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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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Normalizer property of finite groups with almost simple subgroups
Electronic Research Archive, 2022 In this paper, we prove that all Coleman automorphisms of extension of an almost simple group by an abelian group or a simple group are inner. Using our methods we also show that the Coleman automorphisms of 2-power order of an odd order group by an ...
Jingjing Hai , Xian Ling
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GENERATING MAXIMAL SUBGROUPS OF FINITE ALMOST SIMPLE GROUPS
Forum of Mathematics, Sigma, 2020 For a finite group $G$, let $d(G)$ denote the minimal number of elements required to generate $G$. In this paper, we prove sharp upper bounds on $d(H)$ whenever $H$ is a maximal subgroup of a finite almost simple group.
ANDREA LUCCHINI +2 more
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A Simple Classification of Finite Groups of Order p2q2 [PDF]
Mathematics Interdisciplinary Research, 2018 Suppose G is a group of order p2q2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, respectively. In this paper, we show that up to isomorphism, there are four groups of order p2q2 when Q and P are
Aziz Seyyed Hadi +2 more
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