Trait Group 

pub trait Group: AddGroup { }

Represents a Group in abstract algebra.

A group is a fundamental algebraic structure consisting of a set of elements equipped with a single binary operation that satisfies specific axioms.

Mathematical Definition

A set G with a binary operation * is a group if it satisfies:

1. Closure: For all a, b in G, the result a * b is also in G. (Implicit in Rust’s trait system).
2. Associativity: For all a, b, c in G, (a * b) * c = a * (b * c).
3. Identity Element: There exists an element e in G such that for every a in G, e * a = a * e = a.
4. Inverse Element: For each a in G, there exists an element b in G (the inverse of a, denoted a⁻¹) such that a * b = b * a = e.

Crate-Specific Implementation

This Group trait is a general, conceptual trait. In this crate, algebraic structures are typically defined by their primary operation:

• AddGroup: A group under the addition operation (+).
• MulGroup: A group under the multiplication operation (*).

This trait inherits from AddGroup to provide a default group structure based on addition, but it primarily serves as a high-level abstraction.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors

impl<T: AddGroup> Group for T