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2020-06-04T18:46:27+00:00
B. H. Neumann's lemma
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Bound on double coset index in terms of orders of group and subgroup
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Closed subgroup of finite index implies open
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Compact implies every open subgroup has finite index
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Connected implies no proper closed subgroup of finite index
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Finite index implies completely divisibility-closed
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Finite index implies powering-invariant
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Finite index in finite double coset index implies finite double coset index
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Finite index not implies local powering-invariant
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Finitely generated implies every subgroup of finite index has finitely many automorphic subgroups
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Index is multiplicative
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Poincare's theorem
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Schreier's lemma
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Subgroup of finite index has a left transversal that is also a right transversal
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Subgroup of finite index need not be closed in algebraic group
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