TY - JOUR
T1 - The Transfer Ideal under the Action of a Nonmetacyclic Group in the Modular Case
AU - Jia , Panpan
AU - Nan , Jizhu
JO - Communications in Mathematical Research 
VL - 3
SP - 273
EP - 282
PY - 2019
DA - 2019/12
SN - 35
DO - http://doi.org/10.13447/j.1674-5647.2019.03.08
UR - https://global-sci.org/intro/article_detail/cmr/13532.html
KW - invariant, $p$-group, coinvariant, transfer ideal, principal ideal
AB - <p style="text-align: justify;">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.&nbsp;</p>