MTH-301 · 8 pages
Binary operations, groups, subgroups, cosets, and quotient groups.
Contents
Binary operations · Magmas · Semigroups …
Group of units & Equations · Cyclic and abelian groups · Groups of matrices …
The subgroup generated by a set · Symmetric groups · Dihedral groups …
Equivalence relations and partitions · Cosets as equivalence classes · Lagrange's theorem …
Equivalent forms of normality · Quotient groups · The Isomorphism Theorems …
Binary operations and Abelian groups · Function groups and group properties · Inverses and constructed operations
Groups and cyclic equations · Subgroups and homomorphisms · Cyclic groups and permutations …
Lagrange and element orders · Normal subgroups and quotients · Homomorphisms and the first theorem …