Abstract Algebra Reference

Intro to Proofs · Axiom Academy

FORMULA SHEET Abstract Algebra Reference Group and ring axioms, theorems, and proof templates for abstract structures. All cosets of H in G have the same cardinality. Cosets partition G into disjoint subsets. [G : H] is the index of H in G . All subgroups of abelian groups are normal. Every kernel is a normal subgroup. Required to form quotient groups. All cyclic groups are abelian. Every subgroup of a cyclic group is cyclic. has generators (Euler's totient).

This is the written version of the interactive lesson above. See the full Intro to Proofs course.