A Classification of Finite Metahamiltonian p-Groups

A Simple Classification of Finite Groups of Order p2q2

‎Suppose G is a group of order p^2q^2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, ‎respectively‎. ‎In this paper‎, ‎we show that up to isomorphism‎, ‎there are four groups of order p^2q^2 when Q and P are cyclic‎, ‎three groups when Q is a cyclic and P is an elementary ablian group‎, ‎p^2+3p/2+7 groups when Q is an elementary ablian group an...

A Note on Absolute Central Automorphisms of Finite $p$-Groups

Let $G$ be a finite group. The automorphism $sigma$ of a group $G$ is said to be an absolute central automorphism, if for all $xin G$, $x^{-1}x^{sigma}in L(G)$, where $L(G)$ be the absolute centre of $G$. In this paper, we study  some properties of absolute central automorphisms of a given finite $p$-group.

Isoclinic Classification of Some Pairs $(G,G\')$ of $p$-Groups

‎‎The equivalence relation isoclinism partitions the class of all pairs of groups‎ ‎into families‎. ‎In this paper‎, ‎a complete classification of the set of all pairs $(G,G')$ is established‏‎,‎ whenever‎ $G$ is a $p$-group of order at most $p^5‎‏$‎ and ‎$p$ is a prime number greater than 3. Moreover‎, ‎the classification of pairs $(H,H')$ for extra special $p$-groups $H$ is also given.

Finite Groups with p-Sylow Coverings

Pairwise‎ ‎non-commuting elements in finite metacyclic $2$-groups and some finite $p$-groups

Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.