The Herzog-Schönheim conjecture for finite nilpotent groups. (English) Zbl 0553.20009
The Herzog-Schönheim conjecture asserts that if the cosets \(\{a_iK_i: 1\leq i\leq t\}\), \(t>1\), partition a group \(G\) then at least two indices \([G:K_i]\) coincide. We prove the special case of this conjecture where \(G\) is a finite nilpotent group.
Reviewer: Marc A. Berger
MSC:
| 20D15 | Finite nilpotent groups, \(p\)-groups |
| 20D60 | Arithmetic and combinatorial problems involving abstract finite groups |
