# Graduate Seminar Series

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Fri., Aug. 4, 2023 2:15 p.m.
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Location: CW 307.20 and Live Stream
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**Speaker**: Alexander Montoya Ocampo

**Title:** The Macdonald Group (493 kB)

**Abstract:**

According to Johnson (in his famous book Presentations of Groups), an interesting group is a finite group that admits a finite presentation with as many generators as relations. A more widely used synonym is finite group with deficiency zero. These are elusive groups, and few of them are known. A family of such groups was found by I.D. Macdonald. His groups are finite (in most cases) and can be defined by two generators and two relations.

In this talk I will give a brief overview of the Macdonald group, define its 2-Sylow subgroup, and discuss the structure and automorphism group of the latter, as well as the isomorphism problem that arises when considering the family of all these finite 2-groups.

**Live Stream:**