Subgroup proof - is this even true?

[1MileCrash]

Homework Statement

Prove that G cannot have a subgroup H with |H| = n - 1, where n = |G| > 2.

Homework Equations

The Attempt at a Solution

Counter-example, the multiplicative group R and its subgroup, multiplicative group R+. Or, the additive group Z, and its subgroup of integer multiples of 2. What am I missing here? I think this is trivial for finite groups, but they don't say finite groups, they don't say anything.

 

[Dick]

Homework Statement

Prove that G cannot have a subgroup H with |H| = n - 1, where n = |G| > 2.

Homework Equations

The Attempt at a Solution

Counter-example, the multiplicative group R and its subgroup, multiplicative group R+. Or, the additive group Z, and its subgroup of integer multiples of 2. What am I missing here? I think this is trivial for finite groups, but they don't say finite groups, they don't say anything.

Saying n=|G| implies that the group is finite and has order n. Otherwise |H| = n - 1 wouldn't make much sense.

 

[1MileCrash]

OK

Thanks