Class-preserving automorphisms of some finite $p$-groups
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 section 5 of Yadav [Proc. Indian Acad. Sci. (Math. Sci.) 118 (2008), 1-11] and Theorem 4.2 of Kalra and Gumber [Indian J. Pure Appl. Math. 44 (2013), 711-725].
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2014
- DOI:
- 10.48550/arXiv.1407.5921
- arXiv:
- arXiv:1407.5921
- Bibcode:
- 2014arXiv1407.5921S
- Keywords:
-
- Mathematics - Group Theory;
- 20D45;
- 20D15
- E-Print:
- To appear in Proc. Indian Acad. Sci