The Hanna Neumann conjecture for Demushkin groups

Autor: Andrei Jaikin-Zapirain, Mark Shusterman

Publikováno v: Advances in Mathematics. 349:1-28

We confirm the Hanna Neumann conjecture for topologically finitely generated closed subgroups U and W of a nonsolvable Demushkin group G. Namely, we show that ∑ g ∈ U \ G / W d ¯ ( U ∩ g W g − 1 ) ≤ d ¯ ( U ) d ¯ ( W ) where d ¯ ( K ) =

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::003e17b1024c26bb056d008bb3cc10a7
https://doi.org/10.1016/j.aim.2019.04.013

Subgroup properties of Demushkin groups

Autor: Pavel Zalesskii, Ilir Snopce

Publikováno v: Mathematical Proceedings of the Cambridge Philosophical Society. 160:1-9

We prove that a non-solvable Demushkin group satisfies the Greenberg–Stallings property, i.e., if H and K are finitely generated subgroups of a non-solvable Demushkin group G with the property that H ∩ K has finite index in both H and K, then H �

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a2528275a7cccb97dba6e4621669c2ca
https://doi.org/10.1017/s0305004115000481

On subdirect products of free pro-p groups and Demushkin groups of infinite depth

Autor: Hamish Short, Dessislava H. Kochloukova

Publikováno v: Journal of Algebra
Journal of Algebra, Elsevier, 2011, 343 (1), pp.160-172. ⟨10.1016/j.jalgebra.2011.06.012⟩
Journal of Algebra, 2011, 343 (1), pp.160-172. ⟨10.1016/j.jalgebra.2011.06.012⟩

We study subdirect products of free and Demushkin pro-p groups of depth ∞ developing theory similar to the abstract case, see Bridson et al. (2002) [4] . Furthermore we classify when a subdirect product has homological type FP m for some m ⩾ 2 ,

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Free-by-Demushkin pro-p groups

Autor: Dessislava H. Kochloukova, Pavel Zalesskii

Publikováno v: Mathematische Zeitschrift. 249:731-739

We give an example of a short exact sequence 1→N→G→D→1 of pro-p groups such that the cohomological dimension cd(G)=2, G is (topologically) finitely generated, N is a free pro-p group of infinite rank, D is a Demushkin group, for every closed

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https://doi.org/10.1007/s00209-004-0720-6

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