# Thursday 11 Jul 2019: Partitions of a Certain Family of Subgroups of Perm(G)

### Alan Koch - Agnes Scott College, Georgia, USA

Amory C417 14:00-15:00

Let $N$ and $G$ be finite groups of the same order, and let $\mathcal{N}$ be the set of all regular subgroups of $\operatorname{Perm}(G)$ which are isomorphic to $N$ and are normalized by conjugation by elements of $G$ acting via left regular representation. We describe two different partitions of $\mathcal{N}$: a partition into brace classes and a partition into $G$-isomorphism classes, and discuss relationships between them. Examples will be given, particularly in the case $|G|=pq$ with $p,q$ prime.

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