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Factor Groups and Subgroups
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amalgamated associative algebra automorphisms B. H. Neumann basic Lie elements coefficients commutator subgroup conjugate Corollary coset cyclic group cyclically reduced defines an element derivable element of G elements of degree empty word exponent sum extended Schreier system finite index finite number finite order finitely presented follows free Abelian group free factor free group free product freely equal freely reduced word G mod H given graph group G Hence homogeneous homomorphism Hopfian infinite cyclic initial segment integer inverse isomorphic Lemma Let F Let G let H Lie algebra lower central series mapping matrix module monomial Moreover multiplication Neumann Nielsen transformation nilpotent normal subgroup obtain p(gv polynomial quotient group replaced representative system residually finite result rewriting process s-symbols sequence Show single defining relator solve the word subgroup H subgroup of G Suppose syllable length symbols Tietze transformations transformation problem verbal subgroup W(av word problem xv x2 zero