On -conjugate-permutability of Sylow subgroups
Czechoslovak Mathematical Journal (2016)
- Volume: 66, Issue: 1, page 111-117
- ISSN: 0011-4642
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topZhao, Xianhe, and Chen, Ruifang. "On $R$-conjugate-permutability of Sylow subgroups." Czechoslovak Mathematical Journal 66.1 (2016): 111-117. <http://eudml.org/doc/276773>.
@article{Zhao2016,
abstract = {A subgroup $H$ of a finite group $G$ is said to be conjugate-permutable if $HH^\{g\}=H^\{g\}H$ for all $g\in G$. More generaly, if we limit the element $g$ to a subgroup $R$ of $G$, then we say that the subgroup $H$ is $R$-conjugate-permutable. By means of the $R$-conjugate-permutable subgroups, we investigate the relationship between the nilpotence of $G$ and the $R$-conjugate-permutability of the Sylow subgroups of $A$ and $B$ under the condition that $G=AB$, where $A$ and $B$ are subgroups of $G$. Some results known in the literature are improved and generalized in the paper.},
author = {Zhao, Xianhe, Chen, Ruifang},
journal = {Czechoslovak Mathematical Journal},
keywords = {$R$-conjugate-permutable subgroup; nilpotent group; quasinilpotent group; Sylow subgroup},
language = {eng},
number = {1},
pages = {111-117},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On $R$-conjugate-permutability of Sylow subgroups},
url = {http://eudml.org/doc/276773},
volume = {66},
year = {2016},
}
TY - JOUR
AU - Zhao, Xianhe
AU - Chen, Ruifang
TI - On $R$-conjugate-permutability of Sylow subgroups
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 1
SP - 111
EP - 117
AB - A subgroup $H$ of a finite group $G$ is said to be conjugate-permutable if $HH^{g}=H^{g}H$ for all $g\in G$. More generaly, if we limit the element $g$ to a subgroup $R$ of $G$, then we say that the subgroup $H$ is $R$-conjugate-permutable. By means of the $R$-conjugate-permutable subgroups, we investigate the relationship between the nilpotence of $G$ and the $R$-conjugate-permutability of the Sylow subgroups of $A$ and $B$ under the condition that $G=AB$, where $A$ and $B$ are subgroups of $G$. Some results known in the literature are improved and generalized in the paper.
LA - eng
KW - $R$-conjugate-permutable subgroup; nilpotent group; quasinilpotent group; Sylow subgroup
UR - http://eudml.org/doc/276773
ER -
References
top- Baer, R., 10.1090/S0002-9947-1953-0055340-0, Trans. Am. Math. Soc. 75 (1953), 20-47. (1953) MR0055340DOI10.1090/S0002-9947-1953-0055340-0
- Ballester-Bolinches, A., Esteban-Romero, R., Asaad, M., Products of Finite Groups, De Gruyter Expositions in Mathematics 53 Walter de Gruyter, Berlin (2010). (2010) Zbl1206.20019MR2762634
- Foguel, T., 10.1006/jabr.1996.6924, J. Algebra 191 (1997), 235-239. (1997) MR1444498DOI10.1006/jabr.1996.6924
- Huppert, B., Blackburn, N., 10.1007/978-3-642-67997-1_1, Grundlehren der Mathematischen Wissenschaften 243 Springer, Berlin (1982). (1982) MR0662826DOI10.1007/978-3-642-67997-1_1
- Kegel, O. H., 10.1007/BF01650529, Arch. Math. (Basel) 12 (1961), 90-93 German. (1961) MR0133365DOI10.1007/BF01650529
- Murashka, V. I., On partially conjugate-permutable subgroups of finite groups, Probl. Fiz. Mat. Tekh. 14 (2013), 74-78. (2013)
- Robinson, D. J. S., 10.1007/978-1-4684-0128-8, Graduate Texts in Mathematics 80 Springer, Berlin (1982). (1982) Zbl0483.20001MR0648604DOI10.1007/978-1-4684-0128-8
- Wielandt, H., 10.1002/mana.19580180130, Math. Nachr. 18 German (1958), 274-280. (1958) MR0103228DOI10.1002/mana.19580180130
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