This glossary gathers the most important definitions from the public abstract algebra track. Longer entries live on their own subpages so the list can stay readable as it grows.

Current Entries

• Binary Operation: a rule combining two elements of a set and staying inside the same set.
• Identity: an element that leaves every element unchanged under the operation.
• Inverse: an element that combines with a given element to produce the identity.
• Group: a set with a binary operation satisfying closure, associativity, identity, and inverse axioms.
• Subgroup: a subset that is itself a group under the inherited operation.
• Cyclic Group: a group generated by one element.
• Generator: an element or set of elements from which the whole group can be built.
• Permutation: a bijection from a set to itself.
• Coset: a translated copy of a subgroup.
• Normal Subgroup: a subgroup whose left and right cosets coincide.
• Homomorphism: a structure-preserving map between groups.
• Kernel: the set of elements sent to the identity by a homomorphism.
• Factor Group: a quotient group built from cosets of a normal subgroup.
• Simple Group: a group with no nontrivial normal subgroups.