Classification of finite groups with all elements of prime order
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- by Marian Deaconescu PDF
- Proc. Amer. Math. Soc. 106 (1989), 625-629 Request permission
Corrigendum: Proc. Amer. Math. Soc. 117 (1993), 1205-1207.
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
- Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
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- 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 81283
- Guido Zappa, Fondamenti di teoria dei gruppi. Vol. II, Consiglio Nazionale delle Ricerche Monografie Matematiche, vol. 18, Edizioni Cremonese, Rome, 1970 (Italian). MR 0258926
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 625-629
- MSC: Primary 20D20
- DOI: https://doi.org/10.1090/S0002-9939-1989-0969518-2
- MathSciNet review: 969518