A Remark on the Units of Finite Order in The Group Ring of a Finite Group
1974 ◽
Vol 17
(1)
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pp. 129-130
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Keyword(s):
Let G be a group, ZG its integral group ring and U(ZG) the group of units of ZG. The elements ±g∈U(ZG), g∈G, are called the trivial units of ZG. In this note we will proveLet G be a finite group. If ZG contains a non-trivial unit of finite order then it contains infinitely many non-trivial units of finite order.In [1] S. D. Berman has shown that if G is finite then every unit of finite order in ZG is trivial if and only if G is abelian or G is the direct product of a quaternion group of order 8 and an elementary abelian 2-group.
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):
1972 ◽
Vol 15
(4)
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pp. 529-534
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Keyword(s):
1978 ◽
Vol 21
(4)
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pp. 491-496
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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):
1981 ◽
Vol 90
(2)
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pp. 251-257
Keyword(s):
2008 ◽
Vol 3
(1)
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pp. 153-163
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Keyword(s):
1993 ◽
Vol s2-47
(3)
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pp. 433-449