FP3

Question 1

What conditions must be satisfied for something to be a group?

Answer 1

1) Closure - a€G, b€G, a0b€G
2) associativity - for any a,b,c€G, (ab)c=a(bc)
3) identity - for any G there exists e such that for all a€G, a0e=e0a=a
4) inverse - for any a€G, there exists a^-1€G such that a0a^-1=a^-1a=e