Finite groups with odd Sylow normalizers

Finite Groups with p-Sylow Coverings

Groups with the same orders of Sylow normalizers as the Mathieu groups

There exist many characterizations for the sporadic simple groups. In this paper we give two new characterizations for the Mathieu sporadic groups. Let M be a Mathieu group and let p be the greatest prime divisor of |M|. In this paper, we prove that M is uniquely determined by |M| and |NM(P)|, where P ∈ Sylp(M). Also we prove that if G is a finite group, then G ∼= M if and only if for every pri...

Finding Sylow Normalizers in Polynomial Time

Given a set r of permutations of an n-set, let G be the group of permutations generated by r. I f p is any prime, it is known that a Sylow p-subgroup P of G can be found in polynomial time. We show that the normalizer of P can also be found in polynomial time. In particular, given two Sylow p-subgroups of G, all elements conjugating one to the other can be found (as a coset of the normalizer of...

finite groups with p-sylow coverings

POS-groups with some cyclic Sylow subgroups

A finite group G is said to be a POS-group if for each x in G the cardinality of the set {y in G | o(y) = o(x)} is a divisor of the order of G. In this paper we study the structure of POS-groups with some cyclic Sylow subgroups.