On Torsion-Free Groups of Finite Rank
1984 ◽
Vol 36
(6)
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pp. 1067-1080
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Keyword(s):
This paper deals with two conditions which, when stated, appear similar, but when applied to finitely generated solvable groups have very different effect. We first establish the notation before stating these conditions and their implications. If H is a subgroup of a group G, let denote the setWe say G has the isolator property if is a subgroup for all H ≦ G. Groups possessing the isolator property were discussed in [2]. If we define the relation ∼ on the set of subgroups of a given group G by the rule H ∼ K if and only if , then ∼ is an equivalence relation and every equivalence class has a maximal element which may not be unique. If , we call H an isolated subgroup of G.
1999 ◽
Vol 67
(3)
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pp. 399-411
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1992 ◽
Vol 35
(3)
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pp. 390-399
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Keyword(s):
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2015 ◽
Vol 367
(9)
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pp. 6441-6459
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1990 ◽
Vol 48
(3)
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pp. 397-401
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Keyword(s):
2009 ◽
Vol 29
(6)
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pp. 1789-1814
2019 ◽
Vol 29
(06)
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pp. 1083-1112
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