2-Sylow subgroup of rational group is rational if its class is at most two

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Statement

Suppose G is a Finite group (?) that is a Rational group (?) and P is a 2-Sylow subgroup of G. Further, suppose P is a Group of nilpotency class two (?), i.e., the nilpotency class of P is at most two. Then, P is also a rational group.

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