Abstract
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Let
be a finite group
with a Sylow
-subgroup
. We show that the character
table of
determines whether
has maximal nilpotency
class and whether
is a minimal nonabelian group. The latter result is obtained
from a precise classification of the corresponding groups
in terms of their composition
factors. For
-constrained
groups
we prove further that the character table determines whether
can
be generated by two elements.
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Keywords
maximal class, minimal nonabelian, Sylow subgroup, fusion
system, character table
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Mathematical Subject Classification
Primary: 20C15, 20D20
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Milestones
Received: 7 September 2022
Revised: 15 April 2023
Accepted: 26 April 2023
Published: 2 June 2023
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© 2023 The Author(s), under
exclusive license to MSP (Mathematical Sciences Publishers).
Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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