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2019-10-16T01:02:55+00:00
Elementary non-basic facts in group theory
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2008-05-07T22:38:32Z
2454594.4434259
Elementary non-basic facts in group theory
Conjugate-intersection index theorem
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Conjugate-intersection index theorem
Cube map is endomorphism iff abelian (if order is not a multiple of 3)
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Cube map is endomorphism iff abelian (if order is not a multiple of 3)
Inverse map is automorphism iff abelian
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Inverse map is automorphism iff abelian
Normal of order equal to least prime divisor of group order implies central
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Normal of order equal to least prime divisor of group order implies central
Poincare's theorem
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Poincare's theorem
Product of conjugates is proper
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Product of conjugates is proper
Square map is endomorphism iff abelian
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Square map is endomorphism iff abelian
Trivial automorphism group implies trivial or order two
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Trivial automorphism group implies trivial or order two
Union of all conjugates of subgroup of finite index is proper
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Union of all conjugates of subgroup of finite index is proper
Union of two subgroups is not a subgroup unless they are comparable
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Union of two subgroups is not a subgroup unless they are comparable
Every group is a union of cyclic subgroups
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Every group is a union of cyclic subgroups
N-abelian iff abelian (if order is relatively prime to n(n-1))
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N-abelian iff abelian (if order is relatively prime to n(n-1))
Cube map is surjective endomorphism implies abelian
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Cube map is surjective endomorphism implies abelian
Cyclic iff not a union of proper subgroups
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Cyclic iff not a union of proper subgroups
Conjugate-intersection index theorem
0
en
Conjugate-intersection index theorem
Cube map is endomorphism iff abelian (if order is not a multiple of 3)
0
en
Cube map is endomorphism iff abelian (if order is not a multiple of 3)
Inverse map is automorphism iff abelian
0
en
Inverse map is automorphism iff abelian
Normal of order equal to least prime divisor of group order implies central
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en
Normal of order equal to least prime divisor of group order implies central
Poincare's theorem
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en
Poincare's theorem
Product of conjugates is proper
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en
Product of conjugates is proper
Square map is endomorphism iff abelian
0
en
Square map is endomorphism iff abelian
Trivial automorphism group implies trivial or order two
0
en
Trivial automorphism group implies trivial or order two
Union of all conjugates of subgroup of finite index is proper
0
en
Union of all conjugates of subgroup of finite index is proper
Union of two subgroups is not a subgroup unless they are comparable
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en
Union of two subgroups is not a subgroup unless they are comparable
Every group is a union of cyclic subgroups
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Every group is a union of cyclic subgroups
N-abelian iff abelian (if order is relatively prime to n(n-1))
0
en
N-abelian iff abelian (if order is relatively prime to n(n-1))
Cube map is surjective endomorphism implies abelian
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en
Cube map is surjective endomorphism implies abelian
Cyclic iff not a union of proper subgroups
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en
Cyclic iff not a union of proper subgroups