Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is______.

Correct Answer:

7

Solution:

The order of the sub-group must be a factor of the order of the group.

G is a group of 35 elements therefore the Factors of 35 = 1, 5, 7, 35

The order of subgroups as stated in question must be:

(1) largest possible(2) other than G itself the only factor of 35 satisfying these criteria is 7.

Hence the largest possible size of a subgroup of G other than G itself is 7.