Subgroups Permutable with All 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.

groups with all subgroups permutable or soluble

in this paper, we consider locally graded groups in which every non-permutable subgroup is soluble of bounded derived length.

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

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...