Abstract
Let G be a group. An automorphism of G is called an IA-automorphism if it induces the identity mapping on G/γ 2(G), where γ 2(G) is the commutator subgroup of G. Let IA z (G) be the group of those IA-automorphisms, which fix the centre element-wise and let Autcent(G) be the group of central automorphisms, the automorphisms that induce the identity mapping on the central quotient. It can be observed that Autcent(G) = C Aut(G)(IA z (G)). We prove that I A z (G) and IA z (H) are isomorphic for any two finite isoclinic groups G and H. Also, for a finite p-group G, we give a necessary and sufficient condition to ensure that IA z (G)=Autcent(G).
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Acknowledgements
The author is grateful to his supervisor Dr. Manoj K Yadav for his guidance and help in carrying out this work. He thanks the referee for his/her invaluable comments and suggestions, which improved the exposition substantially.
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RAI, P.K. On IA-automorphisms that fix the centre element-wise. Proc Math Sci 124, 169–173 (2014). https://doi.org/10.1007/s12044-014-0175-6
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DOI: https://doi.org/10.1007/s12044-014-0175-6