Principal blocks and $p$-radical groups

Hu, Xiaohan; Zeng, Jiwen

doi:10.1007/s10587-016-0266-x

Geodesic

Parcourir par

Principal blocks and

p

-radical groups

Hu, Xiaohan ; Zeng, Jiwen

Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 431-444.

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

Résumé

Let

G

be a finite group and

k

a field of characteristic

p > 0

. In this paper, we obtain several equivalent conditions to determine whether the principal block

B_{0}

of a finite

p

-solvable group

G

p

-radical, which means that

B_{0}

has the property that

e_{0} (k_{P})^{G}

is semisimple as a

k G

-module, where

P

is a Sylow

p

-subgroup of

G

k_{P}

is the trivial

k P

-module,

(k_{P})^{G}

is the induced module, and

e_{0}

is the block idempotent of

B_{0}

. We also give the complete classification of a finite

p

-solvable group

G

which has not more than three simple

B_{0}

-modules where

B_{0}

p

-radical.

MR Zbl

DOI : 10.1007/s10587-016-0266-x

Classification : 20C05, 20C20
Mots-clés : principal block;

p

-radical group;

p

-radical block

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     author = {Hu, Xiaohan and Zeng, Jiwen},
     title = {Principal blocks and $p$-radical groups},
     journal = {Czechoslovak Mathematical Journal},
     pages = {431--444},
     publisher = {mathdoc},
     volume = {66},
     number = {2},
     year = {2016},
     doi = {10.1007/s10587-016-0266-x},
     mrnumber = {3519612},
     zbl = {06604477},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0266-x/}
}

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Hu, Xiaohan; Zeng, Jiwen. Principal blocks and $p$-radical groups. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 431-444. doi : 10.1007/s10587-016-0266-x. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0266-x/

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