Engineering↗
Subgroups, Direct Products, Cosets and Finite-Group Counting
Handbook treatment of subgroup tests, direct products, coset partitions and the divisibility relation between subgroup and group orders.
Tag
direct product
Every page in the KEVOS library tagged direct product. 7 pages.
Engineering↗
Why Radical Functions Have Soluble Monodromy
Step-by-step structural proof that finite radical constructions have soluble monodromy, using direct products, quotients and commutative kernels.
Engineering↗
Cohomology of Products and Coproducts of Groups
Cohomology of a direct product via Kunneth, cohomology of a free product as a direct sum, Mayer-Vietoris for amalgamated products, and the contrast between the two constructions.
Engineering↗
Direct Products, Factor Congruences and Direct Indecomposability
Direct products, projection homomorphisms, factor congruences as the internal signature of a decomposition, directly indecomposable algebras and the limits of unique factorisation.
Engineering↗
Direct Sums, Products and Split Sequences
Direct sums and direct products of modules, their universal properties, the splitting lemma and equivalent characterisations of split short exact sequences.
Engineering↗
Directly Representable Varieties
Directly representable varieties, McKenzie's theorem that they are congruence-permutable, the classification of their directly indecomposable members, and the connection to the …
Engineering↗
Skew-free Algebras
Skew congruences in direct products, skew-free algebras and varieties, the relationship to congruence permutability and distributivity, and the role in Boolean representations.
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mathematics 387
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