Finite simple groups, prime order elements and width

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• Alex Malcolm (Bristol)
• Thursday 25 February 2021, 15:00-16:00
• http://tinyurl.com/bhamalgsem.

If you have a question about this talk, please contact Lewis Topley.

The generation of finite simple groups has been a thriving area of research for many years. Since it was established that each is generated by a pair of elements, many interesting refinements have followed: for instance, determining the existence of generating pairs of prescribed orders.

More recently the notion of width has provided an additional perspective on generation, measuring how efficiently a chosen subset generates a group. For example we may ask, can every element be written as a product of at most 2, or perhaps 3, elements from a fixed conjugacy class? Answering such questions relies on a range of tools involving subgroup structure and character theory.

In this talk we will examine the width of finite simple groups with respect to elements of a fixed prime order. We will report on sharp bounds for particular families, and answer questions concerning Lie-type groups of unbounded rank.

This talk is part of the Algebra seminar series.

This talk is included in these lists:

• Algebra seminar
• School of Mathematics events
• http://tinyurl.com/bhamalgsem

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