5 papers · 2 filters
Brauer-Fowler Bounds for Elements of Odd Prime Order
Alessandro Dioguardi Burgio, Kıvanç Ersoy, Edoardo Salati
The Brauer--Fowler theorem bounds the order of a finite simple group in terms of the order of the centralizer of an involution. Hartley proved an automorphism version, bounding the…
Mixed identities for simple locally finite groups
Henry Bradford, Kıvanç Ersoy, Jakob Schneider +1
A mixed identity of a group is a nontrivial word with constants that vanishes under every substitution of its variables. We derive lower bounds for the length of mixed identities i…
Inverse ambiguous maps on infinite groups
Sezen Bostan, Kıvanç Ersoy
Let be a group. A bijection is called inverse ambiguous if for every . We prove that every infinite group admits an inverse ambig…
On minimal non-sofic and -non-sofic groups
Kıvanç Ersoy
We investigate structural properties of non-sofic groups, assuming that such groups exist. We introduce and study two classes: minimal non-sofic groups and -non-sofic groups. Fo…
A residually finite analogue of Kegel's theorem on splitting automorphisms
Alfonso Di Bartolo, Kıvanç Ersoy, Giovanni Falcone
Thompson proved that every finite group admitting a fixed-point-free automorphism of prime order is nilpotent, and Kegel showed that the same conclusion holds for finite groups adm…