Consider an elementary abelian group G to be of type (p,p,...,p) for some prime p. A homocyclic group (of rank n) is an abelian group of type (m,m,...,m) i.e.
Think of an elementary abelian group G as having the form (p,p,...,p) where p is a prime number. A homocyclic group (with rank n) has the same structure as a cyclic group, that is,