A Frobenius group is a special type of group in group theory, which is a branch of mathematics. Specifically, a Frobenius group is a group \( G \) that satisfies certain properties related to its subgroups and the action of the group on a set.
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A Frobenius group has a nontrivial proper subgroup satisfying for every , with . Such is a Frobenius complement. The Frobenius kernel theorem turns the identity together with elements outside all conjugates of into a normal subgroup , giving .