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A note on involutive bases of Sylow 2-subgroups of symmetric groups

Pawlik B.

Silesian Journal of Pure and Applied Mathematics

2018

Vol. 8, iss. 1

57--64

The involutive base of a Sylow 2-subgroup Pn(2) of symmetric group S2n is a minimal generating set of this subgroup consisting of elements which are involutions. The Cayley graphs of group Pn(2) on involutive bases may be naturally considered as the undirected ones. The exact number of such bases is not known. In presented paper the necessary condition for base B of group Pn(2) to be involutive is prooved.