Self doubt

Question

Let (g,*) be a group of order p where p is  a prime number then number of proper subgroup is?

I am getting 1 that is identity element,  but somewhere I read, it will be 0. Who is wrong?

Answer 1

It's a debatable topic if we go by the definition of a proper subset then the same definition can be applied to a proper subgroup.

That is G is a group and H is a subgroup H<G is a definition of the proper subgroup, But some authors do not consider trivial subgroup i.e is identity subgroup in a definition of a proper subgroup.

{$\epsilon$} $ \neq $H $\neq$G.

Some authors include some don't answer can be 0 or 1

Comments

I was thinking of same thing, thanks for making it clear

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In One standard book, I read proper sub group is a group containing atleast 2 elements and not all elements. According to this, answer will be 0