Finite Simple Groups

Classification of finite simple groups

by Jamshid Moori

Some results on the partition of groups

by Mohammad Farrokhi Derakhshandeh Ghouchan

Rend. Semin. Mat. Univ. Padova, 125 (2011), 119-146

We investigate some properties of partitions of groups‎. ‎Some‎ ‎information on the structure of nilpotent groups as... more We investigate some properties of partitions of groups‎. ‎Some‎ ‎information on the structure of nilpotent groups as well the‎ ‎embedding of groups with nontrivial partitions into a larger one‎ ‎are discussed‎. ‎Moreover‎, ‎we consider the structure of groups‎ admitting a nontrivial partition with 1‎, 2 or 3 subgroups‎ ‎(considering the whole group) with nontrivial partition and the‎ ‎relation between the number of subgroups with nontrivial‎ ‎partition and the number of primes dividing the order of the‎ ‎group‎. ‎Finally we analyze the relation between the number of‎ ‎components of a nontrivial partition of a group and its order‎.

On Some Classes of Tidy Groups

by Mohammad Farrokhi Derakhshandeh Ghouchan

Algebras, Groups and Geometries, Volume 25 Number 1 (2008) , 109-113
(With A. Erfanian)

‎Let $G$ be a group‎, ‎then $G$ is said to be a tidy group if for‎ ‎every element $x\in G$‎, ‎the set $\{y\in G:\la... more ‎Let $G$ be a group‎, ‎then $G$ is said to be a tidy group if for‎ ‎every element $x\in G$‎, ‎the set $\{y\in G:\la x,y\ra \mbox{ is‎ ‎cyclic}\}$ is a subgroup of $G$‎. ‎The aim of this paper is to‎ ‎investigate the above property for some classes of finite and‎ ‎infinite groups‎. ‎In particular‎, ‎groups with nontrivial partitions‎ ‎and relatively free groups will be discussed in the paper.‎