WordNet-Online
Free dictionary and thesaurus of English. Definitions, synonyms, antonyms and more...
Hint: double-click any word to get it searched!

	Enter your search terms Submit search form
	Web www.wordnet-online.com

Definitions from WordNet

Definitions from the Web

Group Theory

Definition: Group theory is a branch of mathematics that deals with the study of groups, which are sets combined with an operation that satisfy certain properties. It investigates the algebraic structures and symmetries of various mathematical objects.

Senses and Usages:

1. Noun: The mathematical study of groups and their properties.

Example Sentence 1: Group theory is often used in physics to understand the fundamental interactions between particles.

Example Sentence 2: The application of group theory in cryptography ensures secure communication protocols.

2. Noun: A particular algebraic structure consisting of a set and an operation that satisfies the group axioms.

Example Sentence 1: The set of integers under addition is an example of an infinite group.

Example Sentence 2: The symmetric group, denoted as S_n, represents all possible permutations of n elements.

3. Noun: A cluster or gathering of people who share a common interest or purpose.

Example Sentence 1: The book club is a wonderful group where members discuss literature and recommend books to one another.

Example Sentence 2: The protest was organized by a group of activists demanding climate action.

Related Products on Amazon:

• Group Theory Textbooks
• Group Theory Applications
• Group Theory in Physics
• Book Clubs
• Activism