Groups with at most twelve subgroups
Michael C Slattery
TL;DR
This paper classifies all groups with twelve or fewer subgroups, providing a comprehensive list and proof for an entry in the Online Encyclopedia of Integer Sequences.
Contribution
It offers a complete classification of small groups based on their subgroup counts, filling a gap in group theory literature.
Findings
Complete list of groups with ≤12 subgroups
Proofs verifying subgroup counts for each group
Contributions to the OEIS entry on subgroup counts
Abstract
We classify all of the groups with twelve or fewer subgroups. This paper is the proof of the entries in a submission to the Online Encyclopedia of Integer Sequences.
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Taxonomy
TopicsFinite Group Theory Research · Genome Rearrangement Algorithms · History and Theory of Mathematics