The Group of Units of the Integral Group Ring ZS3
1972 ◽
Vol 15
(4)
◽
pp. 529-534
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Keyword(s):
We denote by ZG the integral group ring of the finite group G. We call ±g, for g in G, a trivial unit of ZG. For G abelian, Higman [4] (see also [3, p. 262 ff]) showed that every unit of finite order in ZG is trivial. For arbitrary finite G (indeed, for a torsion group G, not necessarily finite), Higman [4] showed that every unit in ZG is trivial if and only if G is(i) abelian and the order of each element divides 4, or(ii) abelian and the order of each element divides 6, or(iii) the direct product of the quaternion group of order 8 and an abelian group of exponent 2.
1974 ◽
Vol 17
(1)
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pp. 129-130
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Keyword(s):
2008 ◽
Vol 07
(03)
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pp. 393-403
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Keyword(s):
1993 ◽
Vol 35
(3)
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pp. 367-379
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Keyword(s):
Keyword(s):
1976 ◽
Vol 28
(5)
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pp. 954-960
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Keyword(s):
1961 ◽
Vol 57
(3)
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pp. 489-502
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Keyword(s):
2005 ◽
Vol 29
(2)
◽
pp. 363-387
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1969 ◽
Vol 1
(2)
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pp. 245-261
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Keyword(s):
2011 ◽
Vol 21
(04)
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pp. 531-545
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Keyword(s):