What does centralizer and normalizer mean?
Definitions for centralizer and normalizer
cen·tral·iz·er and nor·mal·iz·er
This dictionary definitions page includes all the possible meanings, example usage and translations of the word centralizer and normalizer.
Wikipedia
Centralizer and normalizer
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.
Numerology
Chaldean Numerology
The numerical value of centralizer and normalizer in Chaldean Numerology is: 4
Pythagorean Numerology
The numerical value of centralizer and normalizer in Pythagorean Numerology is: 2
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"centralizer and normalizer." Definitions.net. STANDS4 LLC, 2024. Web. 27 Apr. 2024. <https://www.definitions.net/definition/centralizer+and+normalizer>.
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