Normal subgroups of limit groups of prime index

2016/07/07 by Jhoel S. Gutierrez, Gutierrez, Jhoel S., Thomas Weigel +2
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR

paper · pdf · doi:10.48550/arxiv.1607.02079

13 pages

arxiv created 2016/07/07 · openalex publication_date 2016/07/07 · arxiv updated 2016/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by their study of pro-p limit groups, D.H. Kochloukova and P.A. Zalesskii formulated a question concerning the minimum number of generators d(N) of a normal subgroup N of prime index p in a non-abelian limit group G (cf. Question*). It is shown that the analogous question for the rational rank has an affirmative answer (cf. Thm. A). From this result one may conclude that the original question of D.H. Kochloukova and P.A. Zalesskii has an affirmative answer if the abelianization G^\ab of G is torsion free and d(G)=d(G^\ab) (cf. Cor.~B), or if G has the IF-property (cf. Thm. C).

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