Algebra - Abstract

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

Undefined Sometimes Yes No

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

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

Yes Undefined No (0 has no inverse) Sometimes

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

No Yes Sometimes Undefined

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

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

Undefined Sometimes Yes No

Quiz Questions