Let $G$ be a finite $p$-group of order $p^{n}$ with

$|M(G)|=p^{\\\\\\\\frac{n(n-1)}{2}-t},$ where $M(G)$ is the Schur

multiplier of $G$. Ya.G. Berkovich, X. Zhou, and G. Ellis have

determined the structure of $G$ when $t=0...

\\\\\\\\geq 1$) of a powerful p-group. Our results

extend some of Lubotzky and Mann$^{,}$s (Journal of Algebra, 105

(1987), 484-505.) to nilpotent multipliers. Also, we give some

explicit examples showing the tightness of our results and...

A group is called capable if it is the group of inner automorphisms of a group or equivalently it is a central factor group. This paper verifies the capability of some p-groups....

In this paper G denotes a finite p-group and Γ denotes a simple undirected graph. The orbit graph is a graph whose vertices are non-central orbit under group action of G on a set. Two vertices v1 and v2 are adjacent in the graph if vg v12= where...

abelian p-groups (p prime). We find some numerical inequalities and study

mostly abelian p-groups....

A Remark on the Schur Multiplier of p-Groups...

In this paper, in the class of p-groups of order p4 , we obtain the non-abelian exterior square, the exterior center, the non-abelian tensor square, the tensor center and the third homotopy group of suspension of an Eilenberg–MacLane space k(G,1...

Abstract. If the centre of a group G is trivial, then so is the centre of its automorphism group. We study the structure of the centre of the automorphism group of a group G when the centre of G is a cyclic group.

...

‎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...