On Metanilpotent Varieties of Groups
1970 ◽
Vol 22
(4)
◽
pp. 875-877
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Keyword(s):
Let denote the variety of all groups which are extensions of a nilpotent-of-class-c group by a nilpotent-of-class-d group, and let denote the variety of all metabelian groups. The main result of this paper is the following theorem.THEOREM. Let be a subvariety of which does not contain . Then every -group is an extension of a group of finite exponent by a nilpotent group by a group of finite exponent. In particular, a finitely generated torsion-free -group is a nilpotent-by-finite group.This generalizes the main theorem of Ŝmel′kin [4], where the same result is proved for subvarieties of , where is the variety of abelian groups. See also Lewin and Lewin [2] for a related discussion.
1975 ◽
Vol 27
(6)
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pp. 1355-1360
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1980 ◽
Vol 88
(1)
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pp. 15-31
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Keyword(s):
1995 ◽
Vol 117
(3)
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pp. 431-438
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1969 ◽
Vol 21
◽
pp. 684-701
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Keyword(s):
1996 ◽
Vol 19
(3)
◽
pp. 539-544
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Keyword(s):
1972 ◽
Vol 7
(3)
◽
pp. 437-441
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2018 ◽
Vol 2018
(738)
◽
pp. 281-298
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1956 ◽
Vol 52
(1)
◽
pp. 5-11
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2017 ◽
Vol 101
(2)
◽
pp. 321-328
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