The Schur multiplier of groups of order 𝑝5

Author:

Hatui Sumana1,Kakkar Vipul2,Yadav Manoj K.1

Affiliation:

1. School of Mathematics , Harish-Chandra Research Institute , HBNI, Chhatnag Road, Jhunsi , Allahabad 211019 , India

2. Department of Mathematics , Central University of Rajasthan , NH-8, Bandar Sindri , Ajmer 305817, Rajasthan , India

Abstract

Abstract In this article, we compute the Schur multiplier, non-abelian tensor square and exterior square of non-abelian p-groups of order p 5 {p^{5}} . As an application, we determine the capability of groups of order p 5 {p^{5}} .

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference47 articles.

1. Y. G. Berkovich, On the order of the commutator subgroup and the Schur multiplier of a finite p-group, J. Algebra 144 (1991), no. 2, 269–272.

2. F. R. Beyl, The Schur multiplicator of metacyclic groups, Proc. Amer. Math. Soc. 40 (1973), 413–418.

3. F. R. Beyl, U. Felgner and P. Schmid, On groups occurring as center factor groups, J. Algebra 61 (1979), no. 1, 161–177.

4. F. R. Beyl and M. R. Jones, Addendum: “The Schur multiplicator of metacyclic groups” (Proc. Amer. Math. Soc. 40 (1973), 413–418 by F. R. Beyl), Proc. Amer. Math. Soc. 43 (1974), 251–252.

5. N. Blackburn and L. Evens, Schur multipliers of p-groups, J. Reine Angew. Math. 309 (1979), 100–113.

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