jaj•a•person's notes

Tag: m/thm/group

See Group theory MOC.

54 items with this tag.

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

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