Abstract
Let G be a group, and let \({\mathcal{F}}\) be a family of subgroups of G closed under conjugation. For a positive integer n, let C n denote a cyclic group of order n. We show that if there exists an integer n such that every group in \({\mathcal{F}}\) is C n -cellular and has finite exponent diving n, then the active sum S of \({\mathcal{F}}\) is C n -cellular. We obtain a couple of interesting consequences of this result, using results about cellularity. Finally, we give different proofs of the facts that Coxeter groups are C 2-cellular and that many groups of the form \({\mathrm{SL}(n, q)}\) for n ≥ 3 are C 3-cellular.
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Romero, N. Cyclic cellularity and active sums. Arch. Math. 105, 307–311 (2015). https://doi.org/10.1007/s00013-015-0807-9
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DOI: https://doi.org/10.1007/s00013-015-0807-9