摘要：We show that for $1 \le k \le \sqrt{2\log_3 n}-(5/2)$, the multiset of isomorphism types of $k$-generated subgroups does not determine a group of order at most $n$. This answers a question raised by Tim Gowers in connection with the Group Isomorphism problem
关键词：group theory; nilpotent groups; $p$-groups; group isomorphism problem; algorithms; lower bounds; $k$-generated group; $k$-profile of groups
