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group-theory

Left and right cosets

taught

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Characteristic subgroups Constructing a composition series Group extensions (introduced) Internal direct products Lagrange's theorem Normal subgroups: examples and counterexamples Normality tests (generators, index 2) Quotient groups Simple groups: a first look The commutator subgroup The normalizer of a subgroup Well-definedness of coset multiplication Collapsing cosets into elements Coset representatives and the coset partition Index of a subgroup Normal subgroups When left and right cosets agree Left and right cosets Conjugation Equivalence classes Intersections of subgroups Linear codes as subgroups of (F_2)^n Products of subgroups Subgroups generated by a subset The finite subgroup test Equivalence relations The subgroup test Reflexive and irreflexive Symmetric and antisymmetric The group axioms Transitive

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