University of Birmingham > Talks@bham > Algebra seminar  > Permutation groups, linear groups, and a lack of action

Permutation groups, linear groups, and a lack of action

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The classification of primitive permutation groups possessing a cycle x of length a power of a prime p is a powerful and versatile result. Under the permutation representation of such a group, over a field of characteristic p, the element x acts with a single Jordan block of size p, and the rest of the matrix is the identity.

In recent work I have completed the linear analogue of this result, that is, classified all primitive linear groups over a field of characteristic p possessing a p-element x whose Jordan normal form has a single non-trivial block. I will talk about this and the methods involved.

This talk is part of the Algebra seminar series.

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