Differential equations, Frobenius theorem and local flows on supermanifolds

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Abstract
The classical Frobenius theorem, both in its local and global formulations, is generalised to superanalytic supermanifolds. As an application, it is proved that a coset space G/H (where both G and H are super Lie groups) is a supermanifold. Existence and uniqueness of local flows of tangent vector fields is proved.

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