有限交换群中的极大迷向子模

Maximal Isotropic Submodules in Finite Commutative Groups

设有限群G作用在有限交换群E上,并且E带有一个G-不变的乘法辛型.如果U和V为E的两个极大迷向的G-子模,证明了相伴的两个辛G-模U⊥/U和V⊥/V同构.

Let a finite group G act on a finite commutative group E which is equipped with a G- invariant multiplicative symplectic form. For maximal isotropic G-submoduies U and V of E, it is proved that the associated symplectic G-modules U⊥ /U and V⊥ /V are isomorphic.