Squares of Conjugacy Classes in Alternating Groups

Michael J. Larsen; Pham Huu Tiep

Squares of Conjugacy Classes in Alternating Groups

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arxiv 2305.04806 v1 pith:ASZAZM6B submitted 2023-05-08 math.GR

Michael J. Larsen , Pham Huu Tiep This is my paper · ORCID

classification math.GR

keywords groupsalternatingconjugacyassertingclassclassesconditionsextend

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abstract

We extend to alternating groups $A_n$ several results about symmetric groups asserting that under various conditions on a conjugacy class, or more generally, a normal subset, $C$ of $S_n$, we have $C^2 \supseteq A_n\setminus\{1\}$

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Products of three conjugacy classes in the alternating group
math.GR 2025-05 conditional novelty 8.0 of 10

For large alternating groups, any three conjugacy classes of size at least |G|^(1-δ) multiply to the whole group for a universal small δ.

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