The Hanna Neumann conjecture for Demushkin groups

Andrei Jaikin-Zapirain,Mark Shusterman

doi:10.1016/j.aim.2019.04.013

The Hanna Neumann conjecture for Demushkin groups

Andrei Jaikin-Zapirain, Mark Shusterman

Open Access

https://doi.org/10.1016/j.aim.2019.04.013

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Journal: Advances in Mathematics	Publication Date: Apr 10, 2019
Citations: 5	License type: publisher-specific-oa

Affiliation: Autonomous University of Madrid, Institute of Mathematical Sciences, Carlos III University of Madrid, Tel Aviv University

#Demushkin Group

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Abstract

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/Wd¯(U∩gWg−1)≤d¯(U)d¯(W) where d¯(K)=max⁡{d(K)−1,0} and d(K) is the least cardinality of a topological generating set for the group K.

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