### The number of subgroups of a finite group

Algebra and Geometry Seminar

31st October 2018, 2:30 pm – 3:30 pm

Howard House, 4th Floor Seminar Room

In his 1993 Ann. Math. paper, L. Pyber proves a beautiful upper bound on the

number of isomorphism classes of finite groups of order n. Key to his proof is an upper bound

on the number of subgroups of the symmetric group Sym(n). This upper bound however, is not

sharp, and Pyber makes a conjecture as to what the “correct” bound should be. In this talk,

we will discuss some recent progress on the conjecture, and some consequences in the theory of

random subgroups of a finite group. Joint work with Colva Roney-Dougal.

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