Commutators in finite p-groups
Università degli Studi Trento
38123 Povo (TN)
Tel +39 04 61/281508-1625-1701-3898-1980.
dept.math [at] unitn.it
Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"
- Gustavo A. Fernandez Alcober ((Universidad del País Vasco, Bilbao)
By the positive solution to Ore's conjecture, every element of the commutator subgroup of a finite simple group is itself a commutator. This is far from being true in arbitrary finite groups, the easiest examples being given by finite p-groups, for a prime p. However, under some restrictions, the commutator subgroup of a finite p-group consists entirely of commutators. In this talk, we show that this is always the case if the commutator subgroup can be generated by 2 elements, thus generalising a result of Guralnick who reached the same conclusion with the extra assumption that the group is metabelian. This is joint work with Iker de las Heras.
Referente: Andrea Caranti