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

Panpan Jia & Jizhu Nan

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

  • AMS Subject Headings

13A50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

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

  • BibTex
  • RIS
  • TXT
@Article{CMR-35-273, author = {Jia , Panpan and Nan , Jizhu}, 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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