22 citations · 189 across the 96 of their papers we have counts for
6 papers · 1 filter
Centralizers of coprime automorphisms of finite groups
Cristina Acciarri, Pavel Shumyatsky
Let be an elementary abelian group of order with acting on a finite -group . The following results are proved. If is nilpotent of c…
On profinite groups in which commutators are covered by finitely many subgroups
Cristina Acciarri, Pavel Shumyatsky
For a family of group words we show that if is a profinite group in which all -values are contained in a union of finitely many subgroups with a prescribed property, the…
Fixed points of coprime operator groups
C. Acciarri, P. Shumyatsky
Let m be a positive integer and A an elementary abelian group of order q^r with r greater than or equal to 2 acting on a finite q'-group G. We show that if for some integer d such…
Derived Subgroups of Fixed Points in Profinite Groups
C. Acciarri, A. de Souza Lima, P. Shumyatsky
The main result of this paper is the following theorem. Let q be a prime, A an elementary abelian group of order q^3. Suppose that A acts as a coprime group of automorphisms on a p…
A focal subgroup theorem for outer commutator words
Cristina Acciarri, Gustavo A. Fernández-Alcober, Pavel Shumyatsky
Let be a finite group of order , where is a prime and is not divisible by , and let be a Sylow -subgroup of . If is an outer commutator word, we…
On the exponent of a finite group admitting a fixed-point-free four-group of automorphisms
E. Romano, P. Shumyatsky
Let be a group isomorphic with either , the symmetric group on four symbols, or , the dihedral group of order 8. Let be a normal four-subgroup of and an i…