The order of a simple abelian group is __________
A. infinite
B. real number
C. finite
D. prime
Answer:A
The order of a simple abelian group is __________
A. infinite B. real number C. finite D. prime
Explanation: Let p be the order of g (hence the order of G). As a contradiction, assume that p=ab is a composite number with integers a > 1, b > 1. Then (ga) is a proper normal subgroup of G. This is a contradiction since G is simple. Thus, p must be a prime number.