GROUPS WITH FEW NONPOWER SUBGROUPS

For a group G and $m\ge 1$ , let $G^m$ denote the subgroup generated by the elements $g^m$ , where g runs through G. The subgroups not of the form $G^m$ are the nonpower subgroups of G. We classify the groups with at most nine nonpower subgroups.

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 2024-06, Vol.109 (3), p.529-540
Main Authors: ZHENG, JIWEI, ZHOU, WEI, TAYLOR, D. E.
Format: Article
Language:English
Subjects:
Subgroups
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Description
Summary:For a group G and $m\ge 1$ , let $G^m$ denote the subgroup generated by the elements $g^m$ , where g runs through G. The subgroups not of the form $G^m$ are the nonpower subgroups of G. We classify the groups with at most nine nonpower subgroups.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972723000783