Abstract
Abstract We consider the quotient group T âą ( G ) T(G) of the multiple holomorph by the holomorph of a finite đ-group đș of class two for an odd prime đ. By work of the first-named author, we know that T âą ( G ) T(G) contains a cyclic subgroup of order p r â 1 âą ( p â 1 ) p^{r-1}(p-1) , where p r p^{r} is the exponent of the quotient of đș by its center. In this paper, we shall exhibit examples of đș (with r = 1 r=1 ) such that T âą ( G ) T(G) has order exactly p â 1 p-1 , which is as small as possible.
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