MATH 545 FINALS DEFINITIONS

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Jorge732
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267168
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MATH 545 FINALS DEFINITIONS
Updated:
2014-03-19 21:45:47
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MATH545
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MATH 545 FINALS DEFINITIONS
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  1. Definition 7.4 Let G be a group, H a subgroup of G. If for all
    g ∈ G
    we have gH = Hg, then
    • Let G be a
    • group, H a subgroup of G. If for all g ∈ G we have gH = Hg, then we say H is a
    • normal subgroup of G and write H Δ G.
  2. Definition 7.17 let
    H be a subgroup of a group G. Then
    • let
    • H be a subgroup of a group G. Then NG(H) = { g ∈ G| gHg-1
    • = H} is called the  normalizer of H in G.
  3. Definition 8.4 Let H be a normal subgroup of G.
    • Let H be a
    • normal subgroup of G. Then the group consisting of the cosets of H in G under
    • the operation (aH)(bH)=(ab)H is called the quotient group of G by H, written
    • G/H.
  4. Definition 8.12 Let :G→G’ be a homomorphism.
    • Let :G→G’ be a homomorphism. the
    • image (G)={(x)| x ∈ G} is always a
    • subgroup of G’, and will be equal to G’ itself iff is onto. In this case, G” is said to be a
    • homomorphic image of G.
  5. Definition 9.5 Given two groups G1 and G2
    • Given two groups
    • G1 and G2, the group G1xG2 with the
    • operation defined in the preceding theorem is called the direct product of G1
    • and G2.

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