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group-theory

Internal direct products

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Local knowledge map

Local knowledge map

Applying the classification theorem Finite abelian groups, revisited The First Sylow Theorem (existence) A first look at semidirect products Classification of finite abelian groups Recognizing an internal direct product Small-order classification as a worked recipe Internal direct products Characteristic subgroups Classifying groups of order pq Classifying groups of prime order Constructing a composition series Cyclic groups Group extensions (introduced) Groups of order p² are abelian Normal subgroups: examples and counterexamples Normality tests (generators, index 2) Orders of elements in a direct product Quotient groups Simple groups: a first look The commutator subgroup The normalizer of a subgroup Well-definedness of coset multiplication External direct products Normal subgroups Conjugation Left and right cosets The group axioms

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