Group Theory Fundamentals

An Abelian Group is a group in which the operation is commutative.

A Multiplicative Group is a group in which the operation is multiplication and the set is closed under multiplication, every element has an inverse, and the operation is associative.

An Additive Group is a group in which the operation is addition and the set is closed under addition, every element has an inverse, and the operation is associative.

<p>The order of an element g in a group G is the smallest positive integer n such that $g^n = e$, where e is the identity element of the group.</p> Signup and view all the answers

<p>A subset H of a group G is said to be a subgroup of G if H is also a group under the same operation as G.</p> Signup and view all the answers