What question did this study set out to answer?

The aim is to classify groups that have at most 13 nonpower subgroups, building on previous work for nine subgroups.

February 2, 2026Bulletin of the Australian Mathematical Society0 citationsOpen Access

Groups With at Most 13 Nonpower Subgroups

JZJIWEI ZHENG WZWei ZhouChina University of Political Science and Law DTD. E. TAYLOR

Key Points

The aim is to classify groups that have at most 13 nonpower subgroups, building on previous work for nine subgroups.
Defined nonpower subgroups as those not of the form G^m.
Analyzed the subgroup structure of various groups.
Extended previous classifications to include cases with 10 to 13 nonpower subgroups.
Identified new groups that fit within the classification of having at most 13 nonpower subgroups.
Demonstrated structural properties unique to groups with limited nonpower subgroup counts.

Abstract

Abstract For a group G and m 1, Gᵐ denotes the subgroup generated by the elements gᵐ, where g runs through G. The subgroups not of the form Gᵐ are called nonpower subgroups. We extend the classification of groups with few nonpower subgroups from groups with at most nine nonpower subgroups to groups with at most 13 nonpower subgroups.

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