The group identification problem for $p$-groups of small order

Abstract

We investigate which group-theoretic invariants are powerful in distinguishing among non-isomorphic p-groups. Based on this, we devise an effective algorithm to solve the group identification problem for the $10,494,213$ groups of order $2^9$. We exhibit 56 pairs of groups of order $2^9$ which are difficult to distinguish by invariants.

13 pages