Volume 33, Issue 4
On the Structure of the Augmentation Quotient Group for Some Non-Abelian $p$-Groups

Commun. Math. Res., 33 (2017), pp. 289-303.

Published online: 2019-11

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• Abstract

In this paper, we study the basis of augmentation ideals and the quotient groups of finite non-abelian $p$-group which has a cyclic subgroup of index $p$, where $p$ is an odd prime, and $k$ is greater than or equal to 3. A concrete basis for the augmentation ideal is obtained and then the structure of its quotient groups can be determined.

• Keywords

integral group ring, augmentation ideal, quotient group, $p$-group

16S34, 20C05

zhf3002@163.com (Huifang Zhao)

jznan@163.com (Jizhu Nan)

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• RIS
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@Article{CMR-33-289, author = {Zhao , Huifang and Nan , Jizhu}, title = {On the Structure of the Augmentation Quotient Group for Some Non-Abelian $p$-Groups}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {33}, number = {4}, pages = {289--303}, abstract = {

In this paper, we study the basis of augmentation ideals and the quotient groups of finite non-abelian $p$-group which has a cyclic subgroup of index $p$, where $p$ is an odd prime, and $k$ is greater than or equal to 3. A concrete basis for the augmentation ideal is obtained and then the structure of its quotient groups can be determined.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2017.04.01}, url = {http://global-sci.org/intro/article_detail/cmr/13389.html} }
TY - JOUR T1 - On the Structure of the Augmentation Quotient Group for Some Non-Abelian $p$-Groups AU - Zhao , Huifang AU - Nan , Jizhu JO - Communications in Mathematical Research VL - 4 SP - 289 EP - 303 PY - 2019 DA - 2019/11 SN - 33 DO - http://doi.org/10.13447/j.1674-5647.2017.04.01 UR - https://global-sci.org/intro/article_detail/cmr/13389.html KW - integral group ring, augmentation ideal, quotient group, $p$-group AB -

In this paper, we study the basis of augmentation ideals and the quotient groups of finite non-abelian $p$-group which has a cyclic subgroup of index $p$, where $p$ is an odd prime, and $k$ is greater than or equal to 3. A concrete basis for the augmentation ideal is obtained and then the structure of its quotient groups can be determined.

Huifang Zhao & Jizhu Nan. (2019). On the Structure of the Augmentation Quotient Group for Some Non-Abelian $p$-Groups. Communications in Mathematical Research . 33 (4). 289-303. doi:10.13447/j.1674-5647.2017.04.01
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