gruppenartige

"Gruppenartige" is a term used in the field of mathematics, specifically in the study of groups and their properties. It refers to a mathematical structure that exhibits certain characteristics similar to those of a group, but may not satisfy all the group axioms. The term is often used in the context of semigroups, which are algebraic structures consisting of a set equipped with an associative binary operation.

A semigroup is a set equipped with an associative binary operation. This means that for any elements a, b, and c in the semigroup, the equation (a b) c = a (b c) holds. However, a semigroup does not necessarily have an identity element or inverses for its elements. If a semigroup has an identity element, it is called a monoid.

The term "gruppenartige" can be used to describe semigroups or other algebraic structures that resemble groups in some ways but lack certain group properties. For example, a semigroup might have a subset that forms a group under the same operation, or it might have elements that behave like group elements in certain contexts.

In summary, "gruppenartige" refers to mathematical structures that share some properties with groups but do not fully satisfy the group axioms. These structures are often studied in the context of semigroups and other related algebraic systems.