Groups with Identical $k$-Profiles

Glauberman, George; Grabowski, Łukasz

doi:10.4086/toc.2015.v011a015

Volume 11 (2015) Article 15 pp. 395-401 [Note]

Groups with Identical

$k$ -Profiles

by George Glauberman and Łukasz Grabowski

Received: June 16, 2013
Revised: November 30, 2015
Published: December 23, 2015

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Keywords: group theory, nilpotent groups,

$p$ -groups, group isomorphism problem, algorithms, lower bounds,

$k$ -generated group,

$k$ -profile of groups

Categories: group, nilpotent group, group isomorphism, algorithms, lower bounds, graph isomorphism, note

ACM Classification: F.2.2

AMS Classification: 68Q17, 20D15, 20F69, 68Q25

Abstract: [Plain Text Version]

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.

DOI: 10.4086/toc.2015.v011a015

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