Commun. Math. Res., 35 (2019), pp. 273-282.
Published online: 2019-12
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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.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2019.03.08}, url = {http://global-sci.org/intro/article_detail/cmr/13532.html} }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.