Groups with Identical k-Profiles

Glauberman, George and Grabowski, Łukasz (2015) Groups with Identical k-Profiles. Theory of Computing, 11: 15. pp. 395-401.

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Abstract

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.