We give a detailed description of infinite locally nilpotent groups G such that the index |C_G(x):⟨x⟩| is finite, for every ⟨x⟩⋪G. We are also able to extend our analysis to all non-periodic groups satisfying a variation of our condition, where the requirement of finiteness is replaced with a bound.
A finiteness condition on centralizers in locally nilpotent groups
TORTORA, ANTONIO;TOTA, Maria
2017
Abstract
We give a detailed description of infinite locally nilpotent groups G such that the index |C_G(x):⟨x⟩| is finite, for every ⟨x⟩⋪G. We are also able to extend our analysis to all non-periodic groups satisfying a variation of our condition, where the requirement of finiteness is replaced with a bound.File in questo prodotto:
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A_finiteness_condition_on_centralizers_in_locally_nilpotent_groups.pdf
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