On the number of normal subgroups of an uncountable group
1986 ◽
Vol 41
(3)
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pp. 343-351
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AbstractIn this paper two theorems are proved that give a partial answer to a question posed by G. Behrendt and P. Neumann. Firstly, the existence of a group of cardinality ℵ1 with exactly ℵ1 normal subgroups, yet having a subgroup of index 2 with 2ℵ1 normal subgroups, is consistent with ZFC (the Zermelo-Fraenkel axioms for set theory together with the Axiom of Choice). Secondly, the statement “Every metabelian-by-finite group of cardinality ℵ1 has 2ℵ1 normal subgroups” is consistent with ZFC.
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2018 ◽
2010 ◽
Vol 75
(3)
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pp. 996-1006
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1962 ◽
Vol 20
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pp. 105-168
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2013 ◽
Vol 23
(6)
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pp. 1234-1256
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