Free Subgroups in the Unit Groups of Integral Group Rings
1980 ◽
Vol 32
(6)
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pp. 1342-1352
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Keyword(s):
Rank 2
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Let G be a group, ZG the group ring of G over the ring Z of integers, and U(ZG) the group of units of ZG. One method of investigating U(ZG) is to choose some property of groups and try to determine the groups G such that U(ZG) enjoys that property. For example Sehgal and Zassenhaus [9] have given necessary and sufficient conditions for U(ZG) to be nilpotent (see also [7]), and the same authors have investigated when U(ZG) is an FC (finite-conjugate) group [10]. For a survey of related questions, see [3]. In this paper we consider when U(ZG) contains a free subgroup of rank 2. We conjecture that if this does not happen, then every finite subgroup of G is normal, from which various other conclusions then follow (see Lemma 4).
2013 ◽
Vol 12
(06)
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pp. 1350004
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Keyword(s):
1985 ◽
Vol 31
(3)
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pp. 355-363
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1987 ◽
Vol 30
(1)
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pp. 36-42
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1976 ◽
Vol 28
(5)
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pp. 954-960
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Keyword(s):
1985 ◽
Vol 16
(2)
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pp. 1-9
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2011 ◽
Vol 54
(3)
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pp. 695-709
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Keyword(s):
1982 ◽
Vol 34
(1)
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pp. 233-246
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Keyword(s):
1997 ◽
Vol 39
(1)
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pp. 1-6
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Keyword(s):