Biggs gave a construction of families of Cayley graph of permutation groups with fixed degree and unbounded girth in terms of colored trees.
We give sufficient conditions, in terms of the radius of the tree and number of colors, for the group so defined to contain the alternating group.
The conditions cover infinitely many radii for each number of colors greater than 2, and cover all `small’ cases. This gives theoretical justification for computer experimental results of Exoo and Jajcay.
Biggs colored tree groups containing the alternating group
13.11.2024 09:15 - 10:00
Organiser:
G. Arzhantseva, Ch. Cashen
Location:
SR 06, 1. OG, OMP 1