Algebra - Abstract

The inverse A random element An element that's in every group An element that leaves all others unchanged

Sometimes Undefined Yes No

A group within a group structure A group with fewer elements A subset that is also a group under the same operation Any subset of a group

The number of elements in the group The largest element The identity count The inverse count

Undefined No (0 has no inverse) Sometimes Yes

An algebraic structure with + and · satisfying certain axioms A multiplication of groups A set of numbers A group with two operations

Undefined No Sometimes Yes

a*b = b*a for all a,b a*b ≠ b*a a*a = a a + b = 0

Zero An element a^(-1) such that a*a^(-1) = e The negative of a The opposite of a

Yes Undefined Sometimes No

Quiz Questions