We give a detailed description of infinite locally nilpotent groups G such that the index |C_G(x) : x| is finite, for every xin 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. The research that led to the present paper was partially supported by a grant of the group GNSAGA of INdAMT.
A finiteness condition on centralizers in locally nilpotent groups
Tortora Antonio;
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 xin 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. The research that led to the present paper was partially supported by a grant of the group GNSAGA of INdAMT.File in questo prodotto:
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