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Tuesday 15 May 2018Number Theory Seminar: Construction of Hopf Galois structures via regular subgroups of permutation groups

Cindy Tsang - Tsinghua University, China

H209 14:30-15:30

By a result of C. Greither and B. Pareigis, there is a one-to-one correspondence between Hopf Galois structures on a Galois extension with group $G$ and regular subgroups of $\mbox{Perm}(G)$ normalized by left translations of $G$. By work of N. P. Byott and L. N. Childs, one can in turn construct such subgroups using fixed point free homomorphisms. We shall give a brief review of their work and discuss some generalizations. This is work in progress.

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