Definition

A special type of mapping in mathematics where a structure is transformed into itself while preserving its properties.

Example

In group theory, an automorphism can reveal important symmetries of the group.

Conversation

I was reading about group theory and came across the term automorphism.

Oh, that's interesting! What does it mean exactly?

It’s basically an isomorphism of a set with itself, which sounds complex but is pretty cool.

Got it! That definitely makes sense in the context of math.

Synonyms & Antonyms

Root Explanation

Automorphism is formed from "auto-" (meaning self) and "morphe" (meaning form or shape). The word describes a transformation that is applied to itself, maintaining its original structure while changing its representation.

Memory Tip

Think of 'self' ('auto-') changing its 'form' ('morphe') — that's why automorphism refers to a self-transformation.

Visually Confused Words