A Transfer Result for Powerful Sylow Subgroups

Sylow Subgroups in Parallel

Sylow subgroups are fundamental in the design of asymptotically efficient group-theoretic algorithms, just as they have been in the study of the structure of Ž . finite groups. We present efficient parallel NC algorithms for finding and conjugating Sylow subgroups of permutation groups, as well as for related problems. Polynomial-time solutions to these problems were obtained more than a dozen ...

Some Sylow Subgroups

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.

The Sylow Subgroups of the Symmetric Group

In the Sylow theorems f we learn that if the order of a group 2Í is divisible hj pa (p a prime integer) and not by jo*+1, then 31 contains one and only one set of conjugate subgroups of order pa, and any subgroup of 21 whose order is a power of p is a subgroup of some member of this set of conjugate subgroups of 2Í. These conjugate subgroups may be called the Sylow subgroups of 21. It will be o...

Automorphisms of principal blocks stabilizing Sylow subgroups

Let p be a prime,G a finite group which has a normal p-subgroup containing its own centralizer inG, and R a commutative local ring with residue class field of characteristic p. In this paper, it is shown that if α is an augmented automorphism of RG which fixes a Sylow p-subgroup P of G, there is ρ ∈ Aut(G) such that xαρ = x for all x ∈ P , and αρ is an inner automorphism of RG.