# Naming: How to call a direct product of elementary abelian groups?

Is there an accepted name for abelian groups of the form $\prod_{i=1}^n \mathbb{Z}_{p_i}$ for some primes $p_1,\dotsc,p_n$? (i.e: direct products of cyclic groups of prime orders, or in other words - direct products of elementary abelian groups).

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## 1 Answer

If the primes are distinct, these are the cyclic groups of square-free order.

If the primes are not distinct, these are the abelian groups of square-free exponent.

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On the other hand, direct product of elementary abelian groups is just as good, if not better. –  lhf May 24 '11 at 11:10
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