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Alternating group

In mathematics, an alternating group is the group of even permutations of a finite set. The alternating group on a set of n elements is called the alternating group of degree n, or the alternating group on n letters and denoted by An or Alt(n).

Basic properties, Exceptional isomorphisms & Group homology

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Overview

Basic properties

Conjugacy classes

Automorphism group

Exceptional isomorphisms

Examples

Subgroups

Group homology

Advanced semantic analysis

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Map overview Semantic statistics

Alternating group

Nodes55
Edges54
Triples32
Avg. degree1.96
Density0.036364
Components1

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Alternating group

Top relations

related to Exceptional isomorphisms · 12
Alternating group → A4, A5, A6, A8, F5, Lie, PSL2, PSL4, PSp4, See, There, These
related to H2: Schur multipliers · 5
Alternating group → An, In, Schur, The Schur, These
related to External links · 4
Alternating group → Alternating, Eric, MathWorld, Weisstein
related to The 15 puzzle · 4
Alternating group → A15, A2k, In, It
related to Group homology · 3
Alternating group → However, Note, The
is a · 2
Alternating group → group of even permutations of a finite set, only other normal subgroup a symmetric group has
related to Relation with symmetric group · 2
Alternating group → As, For

Important terminology Word statistics

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Important terminology

group elements alternating a5 symmetric abelianization two order conjugacy automorphism trivial a4 subgroup simple 3-cycles permutations thus groups outer set

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Alternating groupis agroup of even permutations of a finite set0.90text
Alternating groupis aonly other normal subgroup a symmetric group has0.90text
Alternating grouprelated to Exceptional isomorphismsThere0.60section
Alternating grouprelated to Exceptional isomorphismsLie0.60section
Alternating grouprelated to Exceptional isomorphismsThese0.60section
Alternating grouprelated to Exceptional isomorphismsA40.60section
Alternating grouprelated to Exceptional isomorphismsPSL20.60section
Alternating grouprelated to Exceptional isomorphismsA50.60section
Alternating grouprelated to Exceptional isomorphismsSee0.60section
Alternating grouprelated to Exceptional isomorphismsF50.60section
Alternating grouprelated to Exceptional isomorphismsA60.60section
Alternating grouprelated to Exceptional isomorphismsPSp40.60section

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