Finite groups with quasi-dihedral and wreathed 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 $G$.

Invariant Sylow subgroups and solvability of finite groups

Let A and G be finite groups of relatively prime orders and assume that A acts on G via automorphisms. We study how certain conditions on G imply its solvability when we assume the existence of a unique A-invariant Sylow p-subgroup for p equal to 2 or 3. Mathematics Subject Classification (2010). Primary 20D20; Secondary 20D45.

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...