3 citations · 5 across the 6 of their papers we have counts for
9 papers
Metabelian groups: full-rank presentations, randomness and Diophantine problems
Albert Garreta, Leire Legarreta, Alexei Miasnikov +1
We study metabelian groups given by full rank finite presentations in the variety of metabelian groups. We prove that …
Non-inner automorphisms of order p in finite normally constrained p-groups
Norberto Gavioli, Leire Legarreta, Marco Ruscitti
In this paper we study the existence of at least one non-inner automorphism of order p in a finite normally constrained p-group when p is an odd prime.
Non-inner automorphisms of order p in finite p-groups of coclass 3
Marco Ruscitti, Leire Legarreta, Manoj K. Yadav
In this paper we study the existence of at least one non-inner automorphism of order p of a non-abelian finite p-group of coclass 3, where p is a prime integer such that p is diffe…
The existence of non-inner automorphisms of order p in finite thin p-groups
Marco Ruscitti, Leire Legarreta
In this paper we study the existence of at least one non-inner automorphism of order p of a finite thin p-group, for any prime p.
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…
Some finiteness conditions on normalizers or centralizers in groups
Gustavo A. Fernandez-Alcober, Leire Legarreta, Antonio Tortora +1
We consider the following two finiteness conditions on normalizers and centralizers in a group G: (i) |N_G(H):H| is finite for every non-normal subgroup H of G, and (ii) |C_G(x):<x…
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…