Centers of Sylow subgroups and automorphisms

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.

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...