Groups (AQA A-Level Further Maths): Flashcards

Set with operation satisfying CAII axioms

Element that leaves all other elements unchanged when combined

Combining any two elements produces another element in the set

Element that combines with another to produce identity

$a(bc) = (ab)c$ - grouping doesn't affect result

CAII: Closure, Associativity, Identity, Inverses

Number of elements in the group

Smallest $n$ where $x^n = e$ (identity)

Group where $xy = yx$ for all elements (commutative)

$2n$ ($n$ rotations and $n$ reflections)