Cyclic partition for the groups of PSL(2,41) and PSL(2,43)

The ordinary character table and the character table (cha.ta.) of rational representations (ra.repr.) for projective special linear groups (2,41) and (2,43) find in this work to find the cyclic partition for each group

A new characterization of projective special linear groups L3(q)

In this paper, we prove that projective special linear groups L3(q), where 0<q=5k±2 (k∈Z) and q2+q+1 is a~prime number can be uniquely determined by their order and the number of elements with same order.

THE SUBGROUP COMMUTATIVITY DEGREE OF FINITE -GROUPS

The subgroup commutativity degree of a group $G$ is the probability that two subgroups of $G$ commute, or equivalently that the product of two subgroups is again a subgroup. For the dihedral, quasi-dihedral and generalised quaternion groups (all of 2-power cardinality), the subgroup commutativity degree tends to 0 as the size of the group tends to infinity. This also holds for the family of projective special linear groups over fields of even characteristic and for the family of the simple Suzuki groups. In this short note, we show that the family of finite $P$-groups also has this property.

SUBGROUP PERMUTABILITY DEGREE OF PSL(2,pn)

We will compute the subgroup permutability degree of the projective special linear groups PSL(2,pn).