17 citations · 52 across the 13 of their papers we have counts for
3 papers · 2 filters
Some restrictions on normalizers or centralizers in finite p-groups
Gustavo A. Fernandez-Alcober, Leire Legarreta, Antonio Tortora +1
We study three restrictions on normalizers or centralizers in finite p-groups, namely: (i) |N_G(H) : H| <= p^k for every H non-normal in G, (ii) |N_G(<g>) : <g>| <= p^k for every <…
A restriction on centralizers in finite groups
Gustavo A. Fernandez-Alcober, Leire Legarreta, Antonio Tortora +1
For a given m>=1, we consider the finite non-abelian groups G for which |C_G(g):<g>|<=m for every g in G\Z(G). We show that the order of G can be bounded in terms of m and the larg…
On locally graded groups with a word whose values are Engel
Pavel Shumyatsky, Antonio Tortora, Maria Tota
Let m, n be positive integers, v a multilinear commutator word and w = v^m. We prove that if G is a locally graded group in which all w-values are n-Engel, then the verbal subgroup…