17 citations · 28 across the 7 of their papers we have counts for
3 papers · 1 filter
A finiteness condition on centralizers in locally nilpotent groups
Gustavo A. Fernandez-Alcober, Leire Legarreta, Antonio Tortora +1
We give a detailed description of infinite locally nilpotent groups G such that the index |C_G (x) : <x>| is finite, for every non-normal cyclic subgroup <x> of G. We are also able…
A finiteness condition on centralizers in locally finite groups
Gustavo A. Fernandez-Alcober, Leire Legarreta, Antonio Tortora +1
We consider a finiteness condition on centralizers in a group G, namely that |C_G (x) : <x>| is finite for every non-normal cyclic subgroup <x> of G. For periodic groups, this is t…
On varieties of groups satisfying an Engel type identity
P. Shumyatsky, A. Tortora, M. Tota
Let m, n be positive integers, v a multilinear commutator word and w = v^m. Denote by v(G) and w(G) the verbal subgroups of a group G corresponding to v and w, respectively. We pro…