Volume 25, Issue 5
Sub-Cover-Avoidance Properties and the Structure of Finite Groups

Commun. Math. Res., 25 (2009), pp. 418-428.

Published online: 2021-07

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• Abstract

A subgroup $H$ of a group $G$ is said to have the sub-cover-avoidance property in $G$ if there is a chief series $1 = G_0 ≤ G_1 ≤ · · · ≤ G_n = G$, such that $G_{i−1}(H ∩ G_i)\lhd \lhd G$ for every $i = 1, 2, · · · , l$. In this paper, we give some characteristic conditions for a group to be solvable under the assumptions that some subgroups of a group satisfy the sub-cover-avoidance property.

• Keywords

sub-cover-avoidance property, maximal subgroup, Sylow subgroup, solvable group.

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@Article{CMR-25-418, author = {Yangming and Li and and 18197 and and Yangming Li and Kangtai and Peng and and 18198 and and Kangtai Peng}, title = {Sub-Cover-Avoidance Properties and the Structure of Finite Groups}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {5}, pages = {418--428}, abstract = {

A subgroup $H$ of a group $G$ is said to have the sub-cover-avoidance property in $G$ if there is a chief series $1 = G_0 ≤ G_1 ≤ · · · ≤ G_n = G$, such that $G_{i−1}(H ∩ G_i)\lhd \lhd G$ for every $i = 1, 2, · · · , l$. In this paper, we give some characteristic conditions for a group to be solvable under the assumptions that some subgroups of a group satisfy the sub-cover-avoidance property.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19359.html} }
TY - JOUR T1 - Sub-Cover-Avoidance Properties and the Structure of Finite Groups AU - Li , Yangming AU - Peng , Kangtai JO - Communications in Mathematical Research VL - 5 SP - 418 EP - 428 PY - 2021 DA - 2021/07 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19359.html KW - sub-cover-avoidance property, maximal subgroup, Sylow subgroup, solvable group. AB -

A subgroup $H$ of a group $G$ is said to have the sub-cover-avoidance property in $G$ if there is a chief series $1 = G_0 ≤ G_1 ≤ · · · ≤ G_n = G$, such that $G_{i−1}(H ∩ G_i)\lhd \lhd G$ for every $i = 1, 2, · · · , l$. In this paper, we give some characteristic conditions for a group to be solvable under the assumptions that some subgroups of a group satisfy the sub-cover-avoidance property.

YangmingLi & KangtaiPeng. (2021). Sub-Cover-Avoidance Properties and the Structure of Finite Groups. Communications in Mathematical Research . 25 (5). 418-428. doi:
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