4 citations · 10 across the 6 of their papers we have counts for
6 papers
Fibers of automorphic word maps and an application to composition factors
Alexander Bors
In this paper, we study the fibers of "automorphic word maps", a certain generalization of word maps, on finite groups and on nonabelian finite simple groups in particular. As an a…
On finite groups where the order of every automorphism is a cycle length
Alexander Bors
Using Frobenius normal forms of matrices over finite fields as well as the Burnside Basis Theorem, we give a direct proof of Horoševskiĭ's result that every automorphism of a f…
Cycle lengths in finite groups and the size of the solvable radical
Alexander Bors
We prove the following: For any , if a finite group has an automorphism with a cycle of length at least , then the index of the solvable radica…
On the endomorphism monoids of some groups with abelian automorphism group
Alexander Bors
We investigate the endomorphism monoids of certain finite -groups of order first studied by Jonah and Konvisser in 1975 as examples for finite -groups with abelian auto…
Classification of finite group automorphisms with a large cycle
Alexander Bors
Let be a permutation of a finite set . We define to be the largest fraction of elements of lying on a single cycle of . For a finite group , we define $λ(G)…
On the dynamics of endomorphisms of finite groups
Alexander Bors
Aiming at a better understanding of finite groups as finite dynamical systems, we show that by a version of Fitting's Lemma for groups, each state space of an endomorphism of a fin…