On finite groups with semi-dihedral Sylow 2-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.

On rational groups with Sylow 2-subgroups of nilpotency class at most 2

A finite group $G$ is called rational if all its irreducible complex characters are rational valued. In this paper we discuss about rational groups with Sylow 2-subgroups of nilpotency class at most 2 by imposing the solvability and nonsolvability assumption on $G$ and also via nilpotency and nonnilpotency assumption of $G$.

Endotrivial Modules over Groups with Quaternion or Semi-dihedral Sylow 2-subgroup

Suppose that G is a finite group and that k is a field of characteristic p. Endotrivial kG-modules appear in a natural way in many areas surrounding local analysis of finite groups. They were introduced by Dade [14] who classified them in the case that G is an abelian p-group. A complete classification of endotrivial modules over the modular group rings of p-groups was completed just a few year...

Finite Groups with p-Sylow Coverings

A New Finite Simple Group with Abelian 2-sylow Subgroups.

A 2-Sylow subgroup of J is elementary abelian of order 8 and J has no subgroup of index 2. If r is an involution in J, then C(r) = (r) X K, where K _ A5. Let G be a finite group with the following properties: (a) S2-subgroups of G are abelian; (b) G has no subgroup of index 2; and (c) G contains an involution t such that 0(t) = (t) X F, where F A5. Then G is a (new) simple group isomorphic to J...