# Hall satisfies permuting transfer condition

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., Hall subgroup) satisfying a subgroup metaproperty (i.e., permuting transfer condition)

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## Statement

### Statement with symbols

Suppose is a Hall subgroup of a finite group . Suppose, further, that is a subgroup of such that and are permuting subgroups -- in other words, . Then, is a Hall subgroup of .