Group theory:- group theory is a branch of abstract algebra that deals with the study of algebraic structures known as groups. A group is a set of elements together with a binary operation that satisfies certain axioms. Some of the key concepts in group theory include subgroups, cosets, normal subgroups, homomorphisms, and isomorphisms. Here are some notes on these key concepts in group theory: subgroups: a subgroup is a subset of a group that is itself a group under the same operation. H}, where g is an element of g. cosets partition the group into equivalence. = h for all g g. in other words, a normal subgroup is one that is invariant f(a)f(b) for all a, b g. homomorphisms map the group structure of one under conjugation by elements of the group. An isomorphism establishes a one- to-one correspondence between the elements of two groups that preserves the group structure.
