1 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet2 Technion-Israel Institute of Technology3 University of Haifa4 Technion-Israel Institute of Technology5 University of Haifa6 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet
The analog of Lagrangians for symplectic forms over finite groups is studied, motivated by the fact that symplectic G -forms with a normal Lagrangian N◃G are in one-to-one correspondence, up to inflation, with bijective 1-cocycle data on the quotients G/N . This yields a method to construct groups of central type from such quotients, known as Involutive Yang–Baxter groups. Another motivation for the search of normal Lagrangians comes from a non-commutative generalization of Heisenberg liftings that require normality. Although it is true that symplectic forms over finite nilpotent groups always admit Lagrangians, we exhibit an example where none of these subgroups is normal. However, we prove that symplectic forms over nilpotent groups always admit normal Lagrangians if all their p -Sylow subgroups are of order less than p 8 .
London Mathematical Society. Bulletin, 2014, Vol 46, Issue 3, p. 587-599