Sylow numbers and nilpotent Hall 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.

FINITE GROUPS WITH A SYSTEM OF NILPOTENT SUBGROUPS CONTAINING THE SYLOW SUBGROUP By

Let G be a finite group and p an odd prime. By M < G we denote that M is a proper subgroup of G. Put the set Ψ p (G) = {M:M < G, |G : M| 6= a prime power and |G : M|p = 1}. In this paper we investigate the structure of G if every member of Ψ p (G) is nilpotent.

Principal 2-Blocks and Sylow 2-Subgroups

Let G be a finite group with Sylow 2-subgroup P 6 G. Navarro–Tiep–Vallejo have conjectured that the principal 2-block of NG(P) contains exactly one irreducible Brauer character if and only if all odd-degree ordinary irreducible characters in the principal 2-block of G are fixed by a certain Galois automorphism σ. By recent work of Navarro–Vallejo it suffices to show this conjecture holds for al...