Definition

A specific group of elements formed by multiplying a subgroup by a single element from a larger group in mathematics.

Example

In group theory, a coset can help us understand the structure of the group better.

Conversation

Have you ever heard about the concept of a coset in group theory?

No, I haven't! What is it all about?

It's basically a way to describe a subgroup in relation to the whole group, kind of like a copy of it.

That sounds interesting! I might need to look into it more.

Synonyms & Antonyms

Root Explanation

Coset is derived from the term 'coset' in group theory, which is a combination of 'co-' (meaning together) and 'set' (meaning a collection of distinct objects). In mathematics, a coset refers to a set formed by multiplying all elements of a subgroup by a fixed element from the group, thus creating a new set that is related to the original subgroup.

Memory Tip

Think of 'co-' meaning together, and 'set' as a collection — a coset is a collection formed together with elements from a subgroup.

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