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The Nonvanishing First Hochschild Cohomology of Twisted Finite Simple Group Algebras
Let G be a finite simple group and k be an algebraically closed field of prime characteristic dividing the order of G . We show that for all...
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A Criterion for Nonsolvability of a Finite Group and Recognition of Direct Squares of Simple Groups
The spectrum ω(G) of a finite group G is the set of orders of its elements. The following sufficient criterion of nonsolvability is proved: if, among...
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Applications of Finite Non-Abelian Simple Groups to Cryptography in the Quantum Era
The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modeling tools useful in a...
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On Characterization of a Finite Group with Non-simple Socle by the Set of Conjugacy Class Sizes
Let G be a finite group and N ( G ) be the set of its conjugacy class sizes without 1. In the 1980s Thompson conjectured that the equality
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Finite Groups Isospectral to Simple Groups
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...
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Finite Dimensional Group Representations
Algebraic relations among matrices, if any, are encapsulated in their characteristic polynomial. How to decipher this information thus becomes an...
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Characteristic covering numbers of finite simple groups
In the past few decades there has been considerable interest in word maps on groups with emphasis on (non-abelian) finite simple groups. Various...
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Periodic Groups Saturated with Finite Simple Symplectic Groups of Dimension 6 over Fields of Odd Characteristics
We prove that a periodic group is locally finite, if its every finite subgroup lies in a subgroup isomorphic to a simple symplectic group of...
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On groups with chordal power graph, including a classification in the case of finite simple groups
We prove various properties on the structure of groups whose power graph is chordal. Nilpotent groups with this property have been classified by...
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Nonlinear reduction using the extended group finite element method
In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating...
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Unsolvability of Finite Groups Isospectral to the Automorphism Group of the Second Sporadic Janko Group
For a finite group G, the spectrum is the set ω(G) of element orders of the group G. The spectrum of G is closed under divisibility and is therefore...
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On recognition of direct powers of finite simple linear groups by spectrum
The spectrum of a finite group is the set of its element orders. We give an affirmative answer to Problem 20.58(a) from the Kourovka Notebook proving...
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Group of Units of Finite Group Algebras for Groups of Order 24
Let F be a finite field of characteristic p. The structures of the unit groups of group algebras over F for the three groups D 24 , S 4 and SL (2, ℤ 3 ) of...