Se p 20 08 STRONGLY CLOSED SUBGROUPS OF FINITE GROUPS

Strongly closed subgroups of finite groups

This paper gives a complete classification of the finite groups that contain a strongly closed p-subgroup for p any prime.

ar X iv : 0 70 9 . 43 50 v 2 [ m at h . A G ] 1 3 Ju n 20 08 WHICH 3 - MANIFOLD GROUPS ARE KÄHLER GROUPS ?

The question in the title, first raised by Goldman and Donaldson, was partially answered by Reznikov. We give a complete answer, as follows: if G can be realized as both the fundamental group of a closed 3-manifold and of a compact Kähler manifold, then G must be finite—and thus belongs to the well-known list of finite subgroups of O(4).

On semi-$Pi$-property of subgroups of finite group

Let $G$ be a group and $H$ a subgroup of $G$‎. ‎ $H$ is said to have semi-$Pi$-property in $G$ if there is a subgroup $T$ of $G$ such that $G=HT$ and $Hcap T$ has $Pi$-property in $T$‎. ‎In this paper‎, ‎investigating on semi-$Pi$-property of subgroups‎, ‎we shall obtain some new description of finite groups‎.

Classification of finite simple groups whose Sylow 3-subgroups are of order 9

In this paper, without using the classification of finite simple groups, we determine the structure of  finite simple groups whose Sylow 3-subgroups are of the order 9. More precisely, we classify finite simple groups whose Sylow 3-subgroups are elementary abelian of order 9.

Finite Groups with p-Sylow Coverings