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Classification of Finite p-Groups by the Size of Their Schur Multipliers

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Abstract

Let d(G) be the minimum number of elements required to generate a group G. For a group G of order \(p^n\) with a derived subgroup of order \( p^k \) and \(d(G) = d,\) we know the order of the Schur multiplier of G is bounded by \( p^{\frac{1}{2}(d-1)(n-k+2)+1}. \) In this paper, we find the structure of all p-groups that obtains the mentioned bound. Moreover, we show that all of them are capable.

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Acknowledgements

We are grateful to the referee for comments that helped improving the quality of the paper. The second author was supported by the FAPESP grant of Brazil (Process number: 2022/00953-7) at the University of São Paulo.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Damghan University, Damghan, Iran

    Peyman Niroomand

  2. Instituto de Matemática e Estatística da Universidade de São Paulo, Rua do Matão, 1010, São Paulo, SP, CEP: 05586-090, Brazil

    Farangis Johari

Authors
  1. Peyman Niroomand
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  2. Farangis Johari
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Correspondence to Peyman Niroomand.

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Communicated by Shamani Supramaniam.

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Niroomand, P., Johari, F. Classification of Finite p-Groups by the Size of Their Schur Multipliers. Bull. Malays. Math. Sci. Soc. 45, 2137–2150 (2022). https://doi.org/10.1007/s40840-022-01350-9

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