ABSTRACT GROUP Meaning and
Definition
-
An abstract group is a fundamental concept in mathematics that refers to a set of elements or objects, along with a binary operation that specifies how the elements of the set can be combined together. In an abstract group, the elements can be anything that satisfies certain conditions, typically called group axioms. These axioms ensure that the operation is well-defined, meaning that it possesses properties like closure, associativity, identity, and inverses.
One of the key features of an abstract group is that the binary operation used to combine the elements follows specific rules. These rules dictate how the operation interacts with the elements, allowing for the existence of a unique identity element and the possibility of inverses for each element. The operation also needs to be associative, meaning that the order of operations does not affect the result.
Abstract groups serve as a fundamental framework for studying symmetry, transformations, and other related concepts in mathematics. They find applications in various fields including algebra, geometry, number theory, and computer science. Examples of abstract groups include the integers under addition, the group of rotations in a plane, and the set of invertible matrices under matrix multiplication.
Overall, an abstract group provides a formal and rigorous way to understand and analyze the properties and behavior of a set of elements under a binary operation, leading to a deeper understanding of various mathematical structures and phenomena.
Common Misspellings for ABSTRACT GROUP
- zbstract group
- sbstract group
- wbstract group
- qbstract group
- avstract group
- anstract group
- ahstract group
- agstract group
- abatract group
- abztract group
- abxtract group
- abdtract group
- abetract group
- abwtract group
- absrract group
- absfract group
- absgract group
- absyract group
- abs6ract group
- abs5ract group
Etymology of ABSTRACT GROUP
The word "abstract" in the term "abstract group" refers to the concept of a mathematical object that is defined purely by its properties or axioms, rather than being tied to a specific physical or concrete representation.
The term "abstract group" itself is derived from both Latin and Greek origins. The word "abstract" comes from the Latin word "abstractus", which means "drawn away" or "separated". It is formed by combining the prefix "ab-" (meaning "away" or "from") and "-tractus" (meaning "drawn" or "pulled").
The term "group" comes from the Greek word "graphein", which means "to write" or "to draw". It was used in mathematics to refer to a collection of mathematical objects that exhibit certain properties under a specific binary operation, such as addition or multiplication.
Infographic
Add the infographic to your website:
