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Class-preserving automorphisms of some finite p-groups

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Abstract

Let G be a finite p-group of order p 5, where p is a prime. We give necessary and sufficient conditions on G such that G has a non-inner class-preserving automorphism. As a consequence, we give short and alternate proofs of results of Yadav (§5 of Proc. Indian Acad. Sci. (Math. Sci.) 118 (2008) 1–11) and Kalra and Gumber (Theorem 4.2 of Indian J. Pure Appl. Math. 44 (2013) 711–725).

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Acknowledgement

The research of the second author was supported by UGC under the Research Award Scheme.

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Authors and Affiliations

  1. School of Mathematics and Computer Applications, Thapar University, Patiala, 147 004, India

    DEEPAK GUMBER

  2. Department of Applied Sciences and Humanities, Baddi University of Emerging Sciences and Technology, Baddi, 173 205, India

    MAHAK SHARMA

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  1. DEEPAK GUMBER
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  2. MAHAK SHARMA
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Correspondence to DEEPAK GUMBER.

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Communicating Editor: B V Rajarama Bhat

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GUMBER, D., SHARMA, M. Class-preserving automorphisms of some finite p-groups. Proc Math Sci 125, 181–186 (2015). https://doi.org/10.1007/s12044-015-0233-8

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  • DOI: https://doi.org/10.1007/s12044-015-0233-8

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