Details

Autor(en) / Beteiligte

• Li, Xiaogang
• Tian, Yao

Titel

On the automorphism groups of regular maps

Ist Teil von

• Journal of algebraic combinatorics, 2024-01, Vol.59 (1), p.23-35

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2024

Quelle

SpringerLink

Beschreibungen/Notizen

• Let M be an orientably regular (resp. regular) map with the number n vertices. By G + (resp. G ) we denote the group of all orientation-preserving automorphisms (resp. all automorphisms) of M . Let π be the set of prime divisors of n . A Hall π -subgroup of G + (resp. G ) is meant a subgroup such that the prime divisors of its order all lie in π and the primes of its index all lie outside π . It is mainly proved in this paper that (1) suppose that M is an orientably regular map where n is odd. Then G + is solvable and contains a normal Hall π -subgroup; (2) suppose that M is a regular map where n is odd. Then G is solvable if it has no composition factors isomorphic to PSL ( 2 , q ) for any odd prime power q ≠ 3 , and G contains a normal Hall π -subgroup if and only if it has a normal Hall subgroup of odd order.