Groups (AQA A-Level Further Maths): Quizzes

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What mnemonic helps remember the four group axioms?

CAII

What property must the identity element ee satisfy for any element xx in a group?

x∘e=e∘x=xx \circ e = e \circ x = x

What does the closure property ensure for a group?

Combining two elements gives an element in set

What must every element xx in a group have?

An inverse x−1x^{-1} where x∘x−1=ex \circ x^{-1} = e

Which equation defines associativity for elements aa, bb, cc?

a(bc)=(ab)ca(bc) = (ab)c

What is the order of a group?

The number of elements in the group

What is the period of an element xx in a group?

Smallest nn where xn=ex^n = e

How can you identify an abelian group from its Cayley table?

Table is symmetric about leading diagonal

What is the order of dihedral group DnD_n for an nn-sided polygon?

2n2n

What is a generator of a cyclic group?

Element producing all others by repetition

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