On the Cohomological Dimension of Soluble Groups
1981 ◽
Vol 24
(4)
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pp. 385-392
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Keyword(s):
AbstractIt is known that every torsion-free soluble group G of finite Hirsch number hG is countable, and its homological and cohomological dimensions over the integers and rationals satisfy the inequalitiesWe prove that G must be finitely generated if the equality hG = cdQG holds. Moreover, we show that if G is a countable soluble group of finite Hirsch number, but not necessarily torsion-free, and if hG = cdQG, then hḠ = cdQḠ for every homomorphic image Ḡ of G.
1983 ◽
Vol 24
(1)
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pp. 43-52
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Keyword(s):
1974 ◽
Vol 17
(3)
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pp. 305-318
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Keyword(s):
1976 ◽
Vol 28
(6)
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pp. 1302-1310
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1990 ◽
Vol 48
(3)
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pp. 397-401
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Keyword(s):
1984 ◽
Vol 36
(6)
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pp. 1067-1080
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Keyword(s):
1978 ◽
Vol 26
(1)
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pp. 115-125
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Keyword(s):
1972 ◽
Vol 18
(1)
◽
pp. 1-5
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Keyword(s):
2012 ◽
Vol 87
(1)
◽
pp. 152-157
1982 ◽
Vol 26
(3)
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pp. 355-384
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Keyword(s):