2 research outputs found
Orientably-Regular -Maps and Regular -Maps
Given a map with underlying graph , if the set of prime divisors
of is denoted by , then we call the map a {\it
-map}.
An orientably-regular (resp. A regular ) -map is called {\it solvable}
if the group of all orientation-preserving automorphisms (resp. the group
of automorphisms) is solvable; and called {\it normal} if (resp. )
contains a normal -Hall subgroup.
In this paper, it will be proved that orientably-regular -maps are
solvable and normal if and regular -maps are solvable if
and has no sections isomorphic to for some
prime power . In particular, it's shown that a regular -map with
is normal if and only if is isomorphic to a
Sylow -group of .
Moreover, nonnormal -maps will be characterized and some properties and
constructions of normal -maps will be given in respective sections.Comment: 18 pages. arXiv admin note: substantial text overlap with
arXiv:2201.0430