No abstract

The bottom layer of a group is a set of its elements of prime order. A group is called recognizable by bottom layer under additional conditions if it is uniquely restored by bottom layer under these conditions. A group is called almost recognizable by bottom layer under additional conditions, if there are a finite number of pairwise non-isomorphic groups satisfying these conditions, with bottom layer that is the same as that of the group. A group is called unrecognizable by bottom layer under additional conditions if there are an infinite number of pairwise non-isomorphic groups satisfying these conditions, with bottom layer that is the same as that of the group. In the paper we consider examples of groups recognized by bottom layer, by spectrum and, simultaneously, by spectrum and by bottom layer. We have also proved some results of recognizability of groups by bottom layer.