A Necessary Condition for The Residual Nilpotence of HNN-Extensions
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Let G be amultiple HNN-extension of a group A, and let all its associated subgroups be properly contained in some locally nilpotent subgroup of A. We prove that if G is residually nilpotent, then all the associated subgroups are p′-isolated in A for some prime p. Moreover, if q is a prime such that G is residually a q′-torsion-free nilpotent group, then p = q.
Keywords and phrasesmultiple HNN-extension residual nilpotence residual p-finiteness
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