Abstract
We give a sufficient condition on a finite p-group G of nilpotency class 2 so that Aut c (G) = Inn(G), where Aut c (G) and Inn(G) denote the group of all class preserving automorphisms and inner automorphisms of G respectively. Next we prove that if G and H are two isoclinic finite groups (in the sense of P. Hall), then Aut c (G) ≃ Aut c (H). Finally we study class preserving automorphisms of groups of order p 5, p an odd prime and prove that Aut c (G) = Inn(G) for all the groups G of order p 5 except two isoclinism families.
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Yadav, M.K. On automorphisms of some finite p-groups. Proc Math Sci 118, 1–11 (2008). https://doi.org/10.1007/s12044-008-0001-0
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DOI: https://doi.org/10.1007/s12044-008-0001-0