prove or dis prove?

0 ⤊

prove or disprove
every group of prime order is cyclic

2007-11-17 07:19:34 · 2 answers · asked by Dana S 1 in Science & Mathematics ➔ Mathematics

2 answers

Answer at the link below.

2007-11-17 07:36:15 · answer #1 · answered by jgoulden 7 · 0⤊ 0⤋

The order any element must divide the order of the group. But the only divisors of the order of the group are 1 and p, and there can be only one element of order 1. Hence there is at least one element of order p.

But that's what it means for a group to be cyclic.

Q.E.D.

2007-11-18 00:51:35 · answer #2 · answered by Curt Monash 7 · 0⤊ 0⤋