Volume 35, Issue 3
The Transfer Ideal under the Action of a Nonmetacyclic Group in the Modular Case

Commun. Math. Res., 35 (2019), pp. 273-282.

Published online: 2019-12

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• 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.

• Keywords

invariant, $p$-group, coinvariant, transfer ideal, principal ideal

13A50

Panpanjia@mail.dlut.edu.cn (Panpan Jia)

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@Article{CMR-35-273, author = {Panpan and Jia and Panpanjia@mail.dlut.edu.cn and 6048 and School of Mathematics, Dalian University of Technology, Dalian, Liaoning, 116024 and Panpan Jia and Jizhu and Nan and and 6049 and School of Mathematics, Dalian University of Technology, Dalian, Liaoning, 116024 and Jizhu Nan}, title = {The Transfer Ideal under the Action of a Nonmetacyclic Group in the Modular Case}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {35}, number = {3}, pages = {273--282}, 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.

}, 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} }
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 -

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.

Pan-pan Jia & Ji-zhu Nan. (2019). The Transfer Ideal under the Action of a Nonmetacyclic Group in the Modular Case. Communications in Mathematical Research . 35 (3). 273-282. doi:10.13447/j.1674-5647.2019.03.08
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