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- Feb 15, 2012
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You are given a group as a quotient of the free group on two letters, a and b.
the kernel of the surjective homomorphism $F_2 \to G$ is generated by:
$\{a^7,b^6,a^4ba^{-1}b^{-1}\}$
a) prove $G$ is solvable by identifying the derived series:
$G' = [G,G] > G^{\prime \prime} = [G',G'] > \dots $
b) determine the isomorphism class of $G$
(hint: you have 6 to choose from)
the kernel of the surjective homomorphism $F_2 \to G$ is generated by:
$\{a^7,b^6,a^4ba^{-1}b^{-1}\}$
a) prove $G$ is solvable by identifying the derived series:
$G' = [G,G] > G^{\prime \prime} = [G',G'] > \dots $
b) determine the isomorphism class of $G$
(hint: you have 6 to choose from)
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