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The order of the automorphism group of a central product


Author: Kenneth G. Hummel
Journal: Proc. Amer. Math. Soc. 47 (1975), 37-40
DOI: https://doi.org/10.1090/S0002-9939-1975-0352253-1
MathSciNet review: 0352253
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Abstract | References | Additional Information

Abstract: If a $ p$-group $ G$ is the central product of nontrivial subgroups $ H$ and $ A$, where $ A$ is abelian and $ o(H)\vert o(\operatorname{Aut} H)$, then $ o(G)\vert o(\operatorname{Aut} G)$.


References [Enhancements On Off] (What's this?)

  • [1] R. Davitt, The automorphism group of finite $ p$-Abelian $ p$-groups, Illinois J. Math. 16 (1972), 76-85. MR 46 #7378. MR 0308264 (46:7378)
  • [2] R. Faudree, A note on the automorphism group of a $ p$-group, Proc. Amer. Math. Soc. 19 (1968), 1379-1382. MR 40 #1476. MR 0248224 (40:1476)
  • [3] A. D. Otto, Central automorphisms of a finite $ p$-group, Trans. Amer. Math. Soc. 125 (1966), 280-287. MR 34 #4362. MR 0204523 (34:4362)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0352253-1
Keywords: Central product, automorphism group, $ p$-group
Article copyright: © Copyright 1975 American Mathematical Society

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