Volume 37, Issue 4
The $L^*$ Partial Order on the Set of Group Matrices

Commun. Math. Res., 37 (2021), pp. 462-483.

Published online: 2021-08

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• Abstract

In this paper, we use the Löwner partial order and the star partial order to introduce a new partial order (denoted by “$L^*$”) on the set of group matrices, and get some characteristics and properties of the new partial order. In particular, we prove that the $L^*$ partial order is a special kind of the core partial order and it is equivalent to the star partial order under some conditions. We also illustrate its difference from other partial orders with examples and find out under what conditions it is equivalent to other partial orders.

• Keywords

$L^*$ partial order, star partial order, core partial order, Löwner partial order, group matrix.

• AMS Subject Headings

15A09, 15A57, 15A24

• BibTex
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• TXT
@Article{CMR-37-462, author = {Xiaoji and Liu and and 18037 and and Xiaoji Liu and Fang and Gui and and 18038 and and Fang Gui and Hongxing and Wang and and 18039 and and Hongxing Wang}, title = {The $L^*$ Partial Order on the Set of Group Matrices}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {37}, number = {4}, pages = {462--483}, abstract = {

In this paper, we use the Löwner partial order and the star partial order to introduce a new partial order (denoted by “$L^*$”) on the set of group matrices, and get some characteristics and properties of the new partial order. In particular, we prove that the $L^*$ partial order is a special kind of the core partial order and it is equivalent to the star partial order under some conditions. We also illustrate its difference from other partial orders with examples and find out under what conditions it is equivalent to other partial orders.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0012}, url = {http://global-sci.org/intro/article_detail/cmr/19439.html} }
TY - JOUR T1 - The $L^*$ Partial Order on the Set of Group Matrices AU - Liu , Xiaoji AU - Gui , Fang AU - Wang , Hongxing JO - Communications in Mathematical Research VL - 4 SP - 462 EP - 483 PY - 2021 DA - 2021/08 SN - 37 DO - http://doi.org/10.4208/cmr.2021-0012 UR - https://global-sci.org/intro/article_detail/cmr/19439.html KW - $L^*$ partial order, star partial order, core partial order, Löwner partial order, group matrix. AB -

In this paper, we use the Löwner partial order and the star partial order to introduce a new partial order (denoted by “$L^*$”) on the set of group matrices, and get some characteristics and properties of the new partial order. In particular, we prove that the $L^*$ partial order is a special kind of the core partial order and it is equivalent to the star partial order under some conditions. We also illustrate its difference from other partial orders with examples and find out under what conditions it is equivalent to other partial orders.

Xiaoji Liu, Fang Gui & HongxingWang. (2021). The $L^*$ Partial Order on the Set of Group Matrices. Communications in Mathematical Research . 37 (4). 462-483. doi:10.4208/cmr.2021-0012
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