“On pyramidal groups of prime power degree”
Giovedì 18 Gennaio 2024, ore 15:00 - Aula 2BC30 - Martino Garonzi (Università di Brasilia)
Abstract
A Kirkman Triple System (KTS) is called m-pyramidal if there exists a subgroup G of its automorphism group that fixes m points of the KTS and acts regularly on the other points. Such a group G admits a unique conjugacy class C of involutions (elements of order 2) and |C|=m. We call groups with this property m-pyramidal. We prove that, if m is an odd prime power p^k, then every m-pyramidal group is solvable if and only if either m=9 or k is odd. We also determine the sizes of the vertex sets of the m-pyramidal KTS when m is a prime number.
This is a joint work with X. Gao.
