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group
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group

Algebraic set with an invertible, associative internal operation admitting a neutral element

Entitymathematical conceptQ83478

Also known as group (algebra) · group (math) · mathematical group · algebraic group

Instance of
Subclass of

Overview

All data

64 statements · 9% with external sources · numbers in brackets are citations

Has list
Has characteristic
Studied by
Defining formula
  • \begin{aligned}&(\cdot)\colon G\times G\to G\\&\forall x,y,z\in G\colon (x\cdot y)\cdot z=x\cdot(y\cdot z)\\&\exists1\in G\forall x\in G\colon 1\cdot x=x\cdot1=x\\&\forall x\in G\exists y\in G\colon x\cdot y=y\cdot x=1\end{aligned}
Properties for this type
Members / parts
Different from
In defining formula

On other databases

32 identifiers linking group across the web's reference databases