Class-preserving automorphisms of some finite 𝑝-groups

Proceedings Mathematical Sciences

Deepak Gumber¹  Mahak Sharma² 

[1] School of Mathematics and Computer Applications, Thapar University, Patiala 00, India$$;Department of Applied Sciences and Humanities, Baddi University of Emerging Sciences and Technology, Baddi 0, India$$

关键词: Class-preserving automorphism;    𝑝-group;    central automorphism.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let 𝐺 be a finite 𝑝-group of order 𝑝5, 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).

【 授权许可】

Unknown