703 views
0 votes
0 votes
Let G be a group of 52 elements. The largest possible size of a subgroup of G other than G itself is ____.

1 Answer

4 votes
4 votes

Lagranges Theorem – Order of subgroup H divides the order of group G.

Now, we are given order of group is 52. Hence the largest possible size of a subgroup of G other than G itself is basically the largest factor of 52.

The factors of 52 are 1, 2, 4, 13, 26, 52. Hence, all possible sizes of G’s subgroup are 1, 2, 4, 13, 26, 52. But, the question asks for subgroup which isn’t G itself, so correct answer should be 26.

Related questions

1 votes
1 votes
1 answer
1