The automorphism group of a finite metacyclic $p$-group
Author:
Richard M. Davitt
Journal:
Proc. Amer. Math. Soc. 25 (1970), 876-879
MSC:
Primary 20.22
DOI:
https://doi.org/10.1090/S0002-9939-1970-0285594-2
MathSciNet review:
0285594
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper it is shown that if $G$ is a finite non-Abelian metacyclic $p$-group, $p \ne 2$, then the order of $G$ divides the order of the automorphism group of $G$.
- Ralph Faudree, A note on the automorphism group of a $p$-group, Proc. Amer. Math. Soc. 19 (1968), 1379β1382. MR 248224, DOI https://doi.org/10.1090/S0002-9939-1968-0248224-2
- Marshall Hall Jr., The theory of groups, The Macmillan Co., New York, N.Y., 1959. MR 0103215 P. Hall, A contribution to the theory of groups of prime-power orders, Proc. London Math. Soc. (2) 36 (1933), 29-95.
- J. C. Howarth, Some automorphisms of finite nilpotent groups, Proc. Glasgow Math. Assoc. 4 (1960), 204β207 (1960). MR 118766
- O. J. Huval, Mathematical Notes: A Note on the Outer Automorphisms of Finite Nilpotent Groups, Amer. Math. Monthly 73 (1966), no. 2, 174β175. MR 1533639, DOI https://doi.org/10.2307/2313555
- Albert D. Otto, Central automorphisms of a finite$p$-group, Trans. Amer. Math. Soc. 125 (1966), 280β287. MR 204523, DOI https://doi.org/10.1090/S0002-9947-1966-0204523-4
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Keywords:
Finite <IMG WIDTH="16" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img3.gif" ALT="$p$">-groups,
regular,
metacyclic,
automorphism group
Article copyright:
© Copyright 1970
American Mathematical Society