2
$\begingroup$

What is the smallest set of groups $S$, such that for any group $G$ there exists either $H \in S$ or $H = H_1 \times H_2 \times \dots \times H_n$ for $H_i \in S$ such that $G$ and $H$ are isomorphic.

If anything interesting can be said about them, I'd like to hear all cases : with and without infinite groups, with and without infinite products.

Notes. I realize that there may not be a unique such set. My own only idea is the set of all non-abelian groups and cyclic groups of prime order. Also, it should be mentioned that by "small" I mean $\subset$ relation.

  • 0
    Yeah, there is no list of indecomposable groups. "Most" non-abelian groups are indecomposable, and there is no "nice" description of them. I describe how there are a zillion indecomposable groups in this http://math.stackexchange.com/questions/16781/is-there-a-classification-of-all-finite-indecomposable-p-groups2012-08-10

0 Answers 0