On polycyclic groups with isomorphic finite quotients
1978 ◽
Vol 84
(2)
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pp. 235-246
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Keyword(s):
Following P. F. Pickel (5) we write (G) for the set of isomorphism classes of finite quotients of a group G. One of the outstanding problems in the theory of polycyclic groups is to determine whether there can be infinitely many non-isomorphic polycyclic groups G with a given (G). We solve a special case of this problem with our first main result:Theorem 1. Let G be an abelian-by-cyclic polycyclic group. Then the polycyclic-by-finite groups H withlie in only finitely many isomorphism classes.
1976 ◽
Vol 15
(3)
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pp. 347-350
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2017 ◽
Vol 16
(12)
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pp. 1750237
Keyword(s):
2012 ◽
Vol 64
(2)
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pp. 241-253
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1967 ◽
Vol 19
◽
pp. 792-799
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2008 ◽
Vol 60
(3)
◽
pp. 556-571
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Keyword(s):
1960 ◽
Vol 12
◽
pp. 73-100
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Keyword(s):
2016 ◽
Vol 68
(2)
◽
pp. 258-279
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Keyword(s):
1992 ◽
Vol 44
(5)
◽
pp. 897-910
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Keyword(s):
1974 ◽
Vol 11
(1)
◽
pp. 115-120
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