(untitled) (Communications in Mathematical Research, 2019)
Let F_q be a finite field of characteristic p (p eq2) and V_4 a four-dimensional F_q-vector space. In this paper, we mainly determine the structure of the transfer ideal for the ring of polynomials F_q[V_4] under the action of a nonmetacyclic p-group P in the modular case. We prove that the height of the transfer ideal is 1 using the fixed point sets of the elements of order p in P and that the transfer ideal is a principal ideal.