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Rényi Intézet, Algebra Szeminárium
2025. február 3. (hétfő), 10:15-11:15,
Rényi Intézet, Nagyterem (+Zoom)
Pálfy Péter Pál: Groups with large average order of elements
Abstract: Amiri, Jafarian Amiri and Isaacs proved that the average order of elements in a non-cyclic group is always smaller than the average order in the cyclic group of the same order. Herzog, Longobardi and Maj strengthened this result by showing that it is actually at most 7/11 times the average order in the cyclic group. Later several other results were obtained how large this ratio can be for groups in various classes. I will argue that in fact, if this ratio is large, then it is essentially equivalent to the existence of a cyclic subgroup of bounded index. Namely, if the average element order in G is 1/R times the average order in the cyclic group of the same order, then G contains a cyclic subgroup of index less than 9 R log R.
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https://us06web.zoom.us/j/88170589772?pwd=alKno1wb6whK00eKns7wzgezSDg3vi.1
Meeting ID: 881 7058 9772
Passcode: 512995