Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the automorphism group of a finite modular $ p$-group


Authors: Richard M. Davitt and Albert D. Otto
Journal: Proc. Amer. Math. Soc. 35 (1972), 399-404
MSC: Primary 20B25
DOI: https://doi.org/10.1090/S0002-9939-1972-0314946-9
MathSciNet review: 0314946
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper it is shown that if G is a finite non-Abelian modular p-group $ (p > 2)$, then the order of G divides the order of the automorphism group of G.


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

  • [1] J. E. Adney and T. Yen, Automorphisms of a p-group, Illinois J. Math. 9 (1965), 137-143. MR 30 #2072. MR 0171845 (30:2072)
  • [2] R. M. Davitt, The automorphism group of finite p-Abelian p-groups, Illinois J. Math. 16 (1972), 76-85. MR 0308264 (46:7378)
  • [3] R. M. Davitt and A. D. Otto, On the automorphism group of a finite p-group with the central quotient metacyclic, Proc. Amer. Math. Soc. 30 (1971), 467-472. MR 0281797 (43:7511)
  • [4] 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)
  • [5] B. Huppert, Endliche Gruppen. I, Die Grundlehren der math. Wissenschaften, Band 134, Springer-Verlag, Berlin and New York, 1967. MR 37 #302. MR 0224703 (37:302)
  • [6] K. Iwasawa, Über die endlichen und die Verbände ihrer Untergruppen, J. Fac. Sci. Imp. Univ. Tokyo Sect. I 4 (1941), 171-199. MR 3, 193. MR 0005721 (3:193h)
  • [7] F. Napolitani, Sui p-gruppi modulari finiti, Rend. Sem. Mat. Univ. Padova 39 (1967), 296-303. MR 36 #6509. MR 0223461 (36:6509)
  • [8] 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)
  • [9] G. Seitz, On the structure of modular p-groups, unpublished paper.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20B25

Retrieve articles in all journals with MSC: 20B25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0314946-9
Keywords: Finite p-groups, regular, modular, inner automorphisms, central automorphisms
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society