On automorphisms of some finite <Emphasis Type="Italic">p</Emphasis>-groups |
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Authors: | Manoj K Yadav |
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Institution: | (1) School of Mathematics, Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad, 211 019, India |
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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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Keywords: | Finite p-group isoclinism central automorphism class preserving automorphism |
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