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- W1994820072 abstract "Let F be the free product of n groups and let R be a normal subgroup generated (as a normal subgroup) by m elements of F , where m < n . The Main Theorem gives sufficient conditions for families of fewer than n − m subgroups in certain quotients of F / R to generate their free product. This leads to a more direct proof of a result of the first author, that if G is a group having a presentation with n generators and m relators, where m < n , then any generating set for G contains n − m elements that freely generate a free subgroup of G . Another consequence is that an n -generator one-relator group cannot be generated by fewer than n − 1 subgroups each having a non-trivial abelian normal subgroup." @default.
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- W1994820072 date "2007-04-01" @default.
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- W1994820072 title "Free product decompositions in images of certain free products of groups" @default.
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- W1994820072 doi "https://doi.org/10.1016/j.jalgebra.2006.08.008" @default.
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