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)

 

 

Classification of finite groups with all elements of prime order


Author: Marian Deaconescu
Journal: Proc. Amer. Math. Soc. 106 (1989), 625-629
MSC: Primary 20D20
DOI: https://doi.org/10.1090/S0002-9939-1989-0969518-2
Corrigendum: Proc. Amer. Math. Soc. 117 (1993), 1205-1207.
MathSciNet review: 969518
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A finite group having all (nontrivial) elements of prime order must be a $ p$-group of exponent $ p$, or a nonnilpotent group of order $ {p^a}q$, or it is isomorphic to the simple group $ {A_5}$.


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

  • [1] Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
  • [2] B. Huppert, Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
  • [3] Giovanni Zacher, Sull′ordine di un gruppo finito risolubile somma dei suoi sottogruppi di Sylow, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8) 20 (1956), 171–174 (Italian). MR 0081283
  • [4] Guido Zappa, Fondamenti di teoria dei gruppi. Vol. II, Consiglio Nazionale delle Ricerche Monografie Matematiche, vol. 18, Edizioni Cremonese, Rome, 1970 (Italian). MR 0258926

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20D20

Retrieve articles in all journals with MSC: 20D20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0969518-2
Keywords: $ p$-groups, soluble groups
Article copyright: © Copyright 1989 American Mathematical Society