Element structure of extraspecial groups

This article describes the element structure of extraspecial groups. An extraspecial group of order $$p^{1 + 2m}$$, with $$m \ge 1$$ and $$p$$ a prime number, is a non-abelian group $$P$$ of that order such that $$[P,P] = Z(P) = \Phi(P)$$ is a cyclic subgroup of order $$p$$. We can deduce from this that the quotient group is an elementary abelian group of order $$p^{2m}$$.

For every prime $$p$$ and every fixed $$m$$, there are two isomorphism classes of extraspecial groups of order $$p^{1+2m}$$, known as the extraspecial group of '+' and '-' type respectively.