On pro-p analogues of limit groups via extensions of centralizers |
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Authors: | D H Kochloukova P A Zalesskii |
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Institution: | 1. Department of Mathematics, University of Campinas, Cx. P. 6065, Campinas, SP, 13083-970, Brazil 2. Department of Mathematics, University of Bras??lia, Bras??lia, DF, 70910-900, Brazil
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Abstract: | We begin a study of a pro-p analogue of limit groups via extensions of centralizers and call ${\mathcal{L}}$ this new class of pro-p groups. We show that the pro-p groups of ${\mathcal{L}}$ have finite cohomological dimension, type FP ?? and non-positive Euler characteristic. Among the group theoretic properties it is proved that they are free-by-(torsion free nilpotent) and if non-abelian do not have a finitely generated non-trivial normal subgroup of infinite index. Furthermore it is shown that every 2 generated pro-p group in the class ${\mathcal{L}}$ is either free pro-p or abelian. |
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