What does symmetric group mean?
Definitions for symmetric group
sym·met·ric group
This dictionary definitions page includes all the possible meanings, example usage and translations of the word symmetric group.
Wiktionary
symmetric groupnoun
A group whose elements are precisely all of the bijections of some set with itself and whose operation is composition of those bijections.
Wikidata
Symmetric group
In mathematics, the symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself. Since there are n! possible permutations of a set of n symbols, it follows that the order of the symmetric group Sn is n!. Although symmetric groups can be defined on infinite sets as well, this article discusses only the finite symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory. For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set. The symmetric group is important to diverse areas of mathematics such as Galois theory, invariant theory, the representation theory of Lie groups, and combinatorics. Cayley's theorem states that every group G is isomorphic to a subgroup of the symmetric group on G.
Numerology
Chaldean Numerology
The numerical value of symmetric group in Chaldean Numerology is: 8
Pythagorean Numerology
The numerical value of symmetric group in Pythagorean Numerology is: 4
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"symmetric group." Definitions.net. STANDS4 LLC, 2024. Web. 2 May 2024. <https://www.definitions.net/definition/symmetric+group>.
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