Question

Let g be a finite group with more than one element. Show that g has an element of prime order.

Answer 1

be a finite group with more than one element.

Answer 2

Answer:

since order of group is greater than 1 i.e n>1 then

case 1 If n is prime then we are done.

case 2 if n is compostie then n is product of primes so by cauchy theorem if p divides n then there exist an element of order p in the group .

hence g has an element of prime order.