The Transfer Ideal under the Action of a Nonmetacyclic Group in the Modular Case

Abstract

Let $F_q$ be a finite field of characteristic $p$ $(p\neq2)$ 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.