Let \(\mathcal{M}\) 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 \(\mathcal{M}\). Let \(\pi \) be the set of prime divisors of n. A Hall \(\pi \)-subgroup of \(G^+\)(resp. G) is meant a subgroup such that the prime divisors of its order all lie in \(\pi \) and the primes of its index all lie outside \(\pi \). It is mainly proved in this paper that (1) suppose that \(\mathcal{M}\) is an orientably regular map where n is odd. Then \(G^+\) is solvable and contains a normal Hall \(\pi \)-subgroup; (2) suppose that \(\mathcal{M}\) is a regular map where n is odd. Then G is solvable if it has no composition factors isomorphic to \(\hbox {PSL}(2,q)\) for any odd prime power \(q\ne 3\), and G contains a normal Hall \(\pi \)-subgroup if and only if it has a normal Hall subgroup of odd order.

令\(\mathcal{M}\)为具有n 个顶点的可定向正则（或正则）映射。通过\(G^+\)（或G ），我们表示\(\mathcal{M}\)的所有方向保持自同构（或所有自同构）的群。设\(\pi \)为n的素因数集合。\ (G^+\)（分别为G ）的Hall \(\pi \)子群是指其阶的素因数全部位于\(\pi \)及其索引的素数中的子群都位于\(\pi \)之外。本文主要证明：(1)假设\(\mathcal{M}\)是一个有向正则映射，其中n为奇数。则\(G^+\)可解并包含正规霍尔\(\pi \) -子群；(2) 假设\(\mathcal{M}\)是正则映射，其中n为奇数。那么G是可解的，如果它对于任何奇数次幂\(q\ne 3\ )没有与\(\hbox {PSL}(2,q)\)同构的组成因子，并且G包含一个普通霍尔\(\pi \) -子群当且仅当它具有奇数阶的正规霍尔子群。