%0 Journal Article
%T Finite self-similar p-groups with abelian first level stabilizers
%A Zoran Sunic
%J Mathematics
%D 2010
%I arXiv
%R 10.1142/S0218196711006200
%X We determine all finite p-groups that admit a faithful, self-similar action on the p-ary rooted tree such that the first level stabilizer is abelian. A group is in this class if and only if it is a split extension of an elementary abelian p-group by a cyclic group of order p. The proof is based on use of virtual endomorphisms. In this context the result says that if G is a finite p-group with abelian subgroup H of index p, then there exists a virtual endomorphism of G with trivial core and domain H if and only if G is a split extension of H and H is an elementary abelian p-group.
%U http://arxiv.org/abs/1001.1600v4