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Tag: m/thm/group
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Group theory MOC.
54 items with this tag.
2 central extension of a free abelian group
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2 central extension of an elementary abelian 2-group
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A group homomorphism induces a subgroup homomorphism
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ππ and ππ have the same order
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Abelianization
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Alternating group
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Amalgamated free product
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Cauchy's order theorem
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Cayley's theorem
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Central extension of an abelian group
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Centre of a group
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Centre of the general linear group
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Centre of the group ring
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Conjugacy classes of a symmetric group are determined by cycle structure
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Conjugation by an element
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Connected subgroup
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Correspondence between normal subgroups and congruence relations
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Criterion for πβ± = πΚ² in a group
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Crystallographic restriction theorem
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Cyclic central extension of a free abelian group
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Fundamental theorem of cyclic groups
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Group epimorphism
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Group isomorphism theorems
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Group monomorphism
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Group of prime order
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Haar measure
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Haar measure of a compact Lie group
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Kernel of a group homomorphism
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Lagrange's theorem
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Matrix determinant is a homomorphism
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Module isomorphism theorems
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No group is the union of two proper subgroups
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Number of elements of each order in a cyclic group
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Number of elements of order π in a finite group
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Orbit counting lemma
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Orbit-stabilizer theorem
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Order of powers of a group element
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Relationship between IππI and IπIπI
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Semidirect product
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Stabilizer group
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Subgroup
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Subgroup of a free abelian group
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Sylow's theorem
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The conjugate of an n-cycle is an n-cycle
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The group product of elements in commuting subgroups generate a subgroup
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The image of a group homomorphism is a subgroup
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The intersection of normal subgroups is a normal subgroup
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The intersection of subgroups is a subgroup
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The order of a cyclic group equals the order of its generator
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The order of an element and its inverse are the same
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The rank of a transitive group action equals the number of suborbits
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Torsion group with a central cyclic commutator subgroup
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Torsion subgroup of an abelian group
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Unique group involutions are central
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