Finite p-groups with small automorphism group
Jon Gonzalez-Sanchez, Andrei Jaikin-Zapirain

TL;DR
This paper constructs specific finite p-groups demonstrating that their automorphism groups can be arbitrarily small relative to the groups themselves, disproving a longstanding conjecture about automorphism divisibility.
Contribution
It provides a family of finite p-groups with automorphism groups much smaller than the groups, challenging previous assumptions about automorphism divisibility.
Findings
Constructed infinite family of p-groups with automorphism groups much smaller than the groups
Disproved the conjecture that group order divides automorphism group order for all non-abelian p-groups
Showed that the ratio of automorphism group size to group size can tend to zero
Abstract
For each prime we construct a family of finite -groups such that goes to , as goes to infinity. This disproves a well-known conjecture that divides for every non-abelian finite -group .
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Taxonomy
TopicsFinite Group Theory Research · Limits and Structures in Graph Theory · Rings, Modules, and Algebras
