Isotropy in group cohomology

Nir Ben David, Yuval Ginosar, Ehud Meir

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
14 Downloads (Pure)


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 p8.
Original languageEnglish
Pages (from-to)587-599
Number of pages13
JournalBulletin of the London Mathematical Society
Issue number3
Early online date1 Apr 2014
Publication statusPublished - Jun 2014

Bibliographical note

We thank P. Singla and U. Onn for their helpful suggestions.


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