Implement std::ops::Add for a trait

Question

I have a trait like this:

use std::ops::Add;

pub trait GroupElement: Clone + Sized {
    fn plus(&self, b: &Self) -> Self;
}

#[derive(Debug)]
struct G1 {
    value: i32,
}

#[derive(Debug)]
struct G2 {
    value: i32,
}

impl GroupElement for G1 {
    fn plus(&self, b: &Self) -> Self {
        let value = self.value + b.value;
        G1 { value }
    }
}

impl GroupElement for G2 {
    fn plus(&self, b: &Self) -> Self {
        let value = self.value + b.value;
        G2 { value }
    }
}

Now if I wanted to overload the + operator without code duplication I could use a macro to implement the Add trait like this

impl Add for $group_element {
    type Output = Self;

    fn add(self, other: Self) -> Self {
        self.plus(&other)
    }
}

But I want to implement Add for the trait GroupElement so that I can use the generic functions over GroupElement by using the + operator.

impl<T: GroupElement> Add<T> for GroupElement {
    type Output = Self;

    fn add(self, other: T) -> Self {
        self.plus(&other)
    }
}

Above code comlains about GroupElement not having a known size at compile time which I agree with, different groups will have different sizes.

I tried the following code

impl<T: GroupElement> Add<T> for T {
    type Output = T;

    fn add(self, other: T) -> T {
        self.plus(&other)
    }
}

I get error with message type parameter `T` must be used as the type parameter for some local type which seems incorrect since GroupElement is local to my crate.

How should I solve this? The actual implementation of GroupElement is here. Links to G1 and G2.