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Exam 2 Definitions
Fichas del conjunto (10)
- 1Permutation of a set AA function from A to A that is one-to-one and onto.
- 2Permutation group of a set AA set of permutations of A that forms a group under function composition.
- 3Even and Odd PermutationsA permutation that can be expressed as a product of an even number of 2-cycles is called an even permutation. (For odd # odd)
- 4Alternating Group of Degree nThe group of even permutations of n symbols is denoted by A_n and is called the alternating group of degree n.
- 5Group Isomorphism φA one-to-one mapping φ from a group G onto another group that is operation preserving, i.e.,
φ(ab) = φ(a)φ(b) for all a, b in G. - 6Automorphism (of a group)An isomorphism of a group onto itself.
- 7Inner automorphism induced by a, denoted φ_aThe function defined by φ_a(x) = axa-1 for all x in G.
- 8Left coset of H in G containing a, denoted aH Right coset of H in G containing a, denoted Ha Coset representativeGiven a nonempty subset H of a group G. For any element a of G,
a is coset representative. - 9Stabilizer of a PointLet G be a group of permutations of a set S. For each i in S, let (the stabilizer of i in G)
stab_G(i) =
- 10Orbit of a PointLet G be a group of permutations of a set S. For each s in S, let (the orbit of s under G)
orb_G(s) =
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- Fichas sobre Exam 2 Definitions, creado por MathGirl88 el 19/10/2014.
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