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Math Help - residually finite groups

  1. #1
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    residually finite groups

    I have 2 definitions for residually finite groups.

    Definition 1: G is said to be residually finite if for each nontrivial element, x in G, there exists a finite index normal subgroup N_x in G such that x \notin N_x.

    Definition 2: G is said to be residually finite if for each nontrivial element, x \in G, there exists a homomorphism f from G to a finite group, such that f(x) is not the identity.

    I have a problem in proving finite extension of residually finite groups are residually finite.
    I have 1 \longrightarrow K \longrightarrow G \longrightarrow Q \longrightarrow 1, with K is residually finite and Q is finite.

    Can anyone show me where to start or some hints?
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  2. #2
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    can anyone give me some hints or show me how to start?
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