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Geometry of Simple Groups
In this chapter we describe the geometry of simple compact groups. We introduce the adjoint representation, the Casimir operators, and the...
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Shunkov Groups Saturated with Almost Simple Groups
A group G is called a Shunkov group (a conjugate biprimitive finite group) if, for any of its finite subgroups H in the factor group N G ( H )/ H , every...
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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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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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Simple groups with infinite verbal width and the same positive theory as free groups
In this paper we show that there exists an uncountable family of finitely generated simple groups with the same positive theory as any non-abelian...
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Approximate Lattices in Higher-Rank Semi-Simple Groups
We show that strong approximate lattices in higher-rank semi-simple algebraic groups are arithmetic.
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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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Covering Numbers for Simple Algebraic Groups
Let G be a simple algebraic group over an algebraically closed field, and let C be a noncentral conjugacy class of G . The covering number c n ( G , C ) is...
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Counting intrinsic Diophantine approximations in simple algebraic groups
We establish an explicit asymptotic formula for the number of rational solutions of intrinsic Diophantine inequalities on simply-connected simple...
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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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Fundamental Groups of Real Toric Spaces over Simple Polytopes
In this paper we study the cubical stuctures and fundamental groups of real toric spaces. We give an explicit presentation of the fundamental group...
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On recognition of the direct squares of the simple groups with abelian Sylow 2-subgroups
The spectrum of a group is the set of orders of its elements. Finite groups with the same spectra as the direct squares of the finite simple groups...
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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...