The Herzog–Schönheim conjecture for small groups and harmonic subgroups

Leo Margolis, Ofir Schnabel

Onderzoeksoutput: Articlepeer review

3 Citaten (Scopus)

Samenvatting

We prove that the Herzog–Schönheim Conjecture holds for any group G of order smaller than 1440. In other words we show that in any non-trivial coset partition {giUi}i=1n of G there exist distinct 1 ≤ i, j≤ n such that [G: U i] = [G: U j]. We also study interaction between the indices of subgroups having cosets with pairwise trivial intersection and harmonic integers. We prove that if U 1, … , U n are subgroups of G which have pairwise trivially intersecting cosets and n≤ 4 then [G: U 1] , … , [G: U n] are harmonic integers.

Originele taal-2English
Pagina's (van-tot)399-418
Aantal pagina's20
TijdschriftBeiträge zur Algebra und Geometrie
Volume60
Nummer van het tijdschrift3
DOI's
StatusPublished - 1 sep 2019

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