caa a22 4500 388091762 CHVBK 20180307125253.0 cr unu---uuuuu 161130e199910 xx s 000 0 eng 10.1017/S0004972700036339 doi S0004972700036339 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700036339 On groups' with small orders of elements [Elektronische Daten] 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. Copyright © Australian Mathematical Society 1999 Gupta Narain D. Department of Mathematics, University of Manitoba, Winnipeg R3T 2N2, Canada, e-mail: ngupta@cc.umanitoba.ca Mazurov Victor D. Institute of Mathematics, Novosibirsk 630090, Russia, e-mail: mazurov@math.nsc.ru Bulletin of the Australian Mathematical Society Cambridge University Press 60/2(1999-10), 197-205 0004-9727 60:2<197 1999 60 BAZ https://doi.org/10.1017/S0004972700036339 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700036339 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gupta Narain D. Department of Mathematics, University of Manitoba, Winnipeg R3T 2N2, Canada, e-mail: ngupta@cc.umanitoba.ca NATIONALLICENCE 700 1- Mazurov Victor D. Institute of Mathematics, Novosibirsk 630090, Russia, e-mail: mazurov@math.nsc.ru NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 60/2(1999-10), 197-205 0004-9727 60:2<197 1999 60 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge