On $R$-conjugate-permutability of Sylow subgroups

Zhao, Xianhe; Chen, Ruifang

doi:10.1007/s10587-016-0243-4

Geodesic

Parcourir par

R

-conjugate-permutability of Sylow subgroups

Zhao, Xianhe ; Chen, Ruifang

Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 111-117.

Voir la notice de l'article dans Czech Digital Mathematics Library

Résumé

A subgroup

H

of a finite group

G

is said to be conjugate-permutable if

H H^{g} = H^{g} H

for all

g \in G

. More generaly, if we limit the element

g

to a subgroup

R

G

, then we say that the subgroup

H

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 = A B

, where

A

and

B

are subgroups of

G

. Some results known in the literature are improved and generalized in the paper.

MR Zbl

DOI : 10.1007/s10587-016-0243-4

Classification : 20D10, 20D20
Mots-clés :

R

-conjugate-permutable subgroup; nilpotent group; quasinilpotent group; Sylow subgroup

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     author = {Zhao, Xianhe and Chen, Ruifang},
     title = {On $R$-conjugate-permutability of {Sylow} subgroups},
     journal = {Czechoslovak Mathematical Journal},
     pages = {111--117},
     publisher = {mathdoc},
     volume = {66},
     number = {1},
     year = {2016},
     doi = {10.1007/s10587-016-0243-4},
     mrnumber = {3483226},
     zbl = {06587877},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0243-4/}
}

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Zhao, Xianhe; Chen, Ruifang. On $R$-conjugate-permutability of Sylow subgroups. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 111-117. doi : 10.1007/s10587-016-0243-4. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0243-4/

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