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.

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.

‎let $g$ be a group and $a=aut(g)$ be the group of automorphisms of‎ ‎$g$‎. ‎then the element $[g,alpha]=g^{-1}alpha(g)$ is an‎ ‎autocommutator of $gin g$ and $alphain a$‎. ‎also‎, ‎the‎ autocommutator subgroup of g is defined to be‎ ‎$k(g)=langle[g,alpha]|gin g‎, ‎alphain arangle$‎, ‎which is a‎ ‎characteristic subgroup of $g$ containing the derived subgroup‎ ‎$g'$ of $g$‎. ‎a group is defined...

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.

Roussel and Rubio proved a lemma which is essential in the proof of the Strong Perfect Graph Theorem. We give a new short proof of the main case of this lemma. In this note, we also give a short proof of Hayward’s decomposition theorem for weakly chordal graphs, relying on a Roussel–Rubio-type lemma. We recall how Roussel–Rubio-type lemmas yield very short proofs of the existence of even pairs ...

We will extend Reed's Semi-Strong Perfect Graph Theorem by proving that unbreakable C 5-free graphs diierent from a C 6 and its complement have unique P 4-structure.