On the exponent of the non-abelian tensor square and related constructions of finite p-groups

Abstract: Abstract: If $F$ is an operator in the class of finite groups, it is quite natural to ask whether or not it is then possible to bound the exponent of $F(G)$ in terms of the exponent of G only, where G is a finite group. In 1991, N. Rocco introduced the operator $\nu$ which associates to every group G a certain extension of the non-abelian tensor square $G\otimes G$ by $G\times G$.

In this talk we will give an exposition of a joint work with Raimundo Bastos, Emerson de Melo and Nathalia Goncalves, where we deal with the restriction of $\nu$ to the class of finite p-groups, for p a prime. More precisely, we address the problem to determine bounds for the exponent of $\nu(G)$ and $G\otimes G$ when $G$ is a finite p-group. The obtained bounds improve some existing ones and depend on the exponent of $G$ and either on the nilpotency class or on the coclass of the finite p-group $G$.

group theoryrings and algebras

Audience: researchers in the topic

Al@Bicocca take-away