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In this article, we compute the Schur multiplier, non-abelian tensor square and exterior square of non-abelian p-groups of order p5. As an application, we determine the capability of groups of order p5. [ABSTRACT FROM AUTHOR]

In this article, we compute the Schur multiplier, non-abelian tensor square and exterior square of non-abelian p-groups of order p5. As an application, we determine the capability of groups of order p5. [ABSTRACT FROM AUTHOR]

For a group G and a subset X of G , the commuting graph of X , denoted by Γ (X) = ℭ (D (G) , X) is the graph whose vertex set is X and any two vertices u and v in X are adjacent if and only if they commute in G. In this paper, certain properties of the commuting graph of generalized dihedral groups have been studied. [ABSTRACT FROM AUTHOR]