# On families of nilpotent subgroups and associated coset posets

@inproceedings{Gritschacher2021OnFO, title={On families of nilpotent subgroups and associated coset posets}, author={Simon Gritschacher and Bernardo Villarreal}, year={2021} }

We study some properties of the coset poset associated with the family of subgroups of class ≤ 2 of a nilpotent group of class ≤ 3. We prove that under certain assumptions on the group the coset poset is simply-connected if and only if the group is 2-Engel, and 2-connected if and only if the group is nilpotent of class 2 or less. We determine the homotopy type of the coset poset for the group of 4 × 4 upper unitriangular matrices over Fp, and for the Burnside groups of exponent 3.

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