# Definitions for normalisernor·malis·er

### Princeton's WordNetRate this definition:0.0 / 0 votes

1. normalizer, normalisernoun

a person who normalizes

### WikipediaRate this definition:0.0 / 0 votes

1. normaliser

In mathematics, especially group theory, the centralizer (also called commutant) of a subset S in a group G is the set of elements C G ( S ) {\displaystyle \mathrm {C} _{G}(S)} of G such that each member g ∈ C G ( S ) {\displaystyle g\in \mathrm {C} _{G}(S)} commutes with each element of S, or equivalently, such that conjugation by g {\displaystyle g} leaves each element of S fixed. The normalizer of S in G is the set of elements N G ( S ) {\displaystyle \mathrm {N} _{G}(S)} of G that satisfy the weaker condition of leaving the set S ⊆ G {\displaystyle S\subseteq G} fixed under conjugation. The centralizer and normalizer of S are subgroups of G. Many techniques in group theory are based on studying the centralizers and normalizers of suitable subsets S. Suitably formulated, the definitions also apply to semigroups. In ring theory, the centralizer of a subset of a ring is defined with respect to the semigroup (multiplication) operation of the ring. The centralizer of a subset of a ring R is a subring of R. This article also deals with centralizers and normalizers in a Lie algebra. The idealizer in a semigroup or ring is another construction that is in the same vein as the centralizer and normalizer.

### ChatGPTRate this definition:0.0 / 0 votes

1. normaliser

In mathematics, particularly in group theory, the normalizer of a subset S of a group G is the largest subgroup of G in which S is a normal subgroup. It is usually denoted as N_G(S). This concept is used to define various important notions in group theory and its applications in topology, number theory, and algebraic geometry.

### Numerology

1. Chaldean Numerology

The numerical value of normaliser in Chaldean Numerology is: 6

2. Pythagorean Numerology

The numerical value of normaliser in Pythagorean Numerology is: 7

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"normaliser." Definitions.net. STANDS4 LLC, 2024. Web. 4 Aug. 2024. <https://www.definitions.net/definition/normaliser>.

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