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On groups’ with small orders of elements

Published online by Cambridge University Press:  17 April 2009

Narain D. Gupta  and
Victor D. Mazurov
Narain D. Gupta
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg R3T 2N2, Canada, e-mail: ngupta@cc.umanitoba.ca
Victor D. Mazurov
Affiliation:
Institute of Mathematics, Novosibirsk 630090, Russia, e-mail: mazurov@math.nsc.ru
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For a periodic group G, denote by ω(G) the set of orders of elements in G. We prove that if ω(G) is a proper subset of the set {1, 2, 3, 4, 5} then either G is locally finite or G contains a nilpotent normal subgroup N such that G/N is a 5-group.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 2 , October 1999 , pp. 197 - 205
Copyright
Copyright © Australian Mathematical Society 1999

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