  The famous T. Suffridge polynomials have many extremal properties: the
maximality of coefficients when the leading coefficient is maximal; the zeros
of the derivative are located on the unit circle; the maximum radius of
stretching the unit disk with the schlicht normalization $F(0)=0$, $F'(0)=1$;
the maximum size of the unit disk contraction in the direction of the real axis
for univalent polynomials with the normalization $F(0)=0$, $F(1)=1.$ However,
under the standard symmetrization method $\sqrt[T]{F(z^T)}$, these polynomials
go to functions, which are not polynomials. How can we construct the
polynomials with fold symmetry that have properties similar to those of the
Suffridge polynomial? What values will the corresponding extremal quantities
take in the above-mentioned extremal problems? The paper is devoted to solving
these questions for the case of the trinomials $F(z)=z+az^{1+T}+bz^{1+2T}$.
Also, there are suggested hypotheses for the general case in the work.
