# 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.
 Author: Jorge732 ID: 267168 Card Set: MATH 545 FINALS DEFINITIONS Updated: 2014-03-20 01:45:47 Tags: MATH545 Folders: Description: MATH 545 FINALS DEFINITIONS Show Answers: