When the Wedderburn decomposition of the semisimple group algebra FqG implies that of Fq(G × C2)?
Serdica Mathematical Journal, Tome 46 (2021) no. 3, pp. 253-260
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In this short note we give a condition under which the Wedderburn decomposition (WD) of the semisimple group algebra \(F_q(G\times C_2)\) can be directly deduced from the WD of the semisimple group algebra \(F_qG\), where \(F_q\) is a finite field with char\((F_q)>2\), \(G\) is an arbitrary finite group and \(C_2\) is a group of order 2. To complement the abstract theory with an example, we determine the WD of the semisimple group algebra \(F_q(A_5\times C_2)\), where \(A_5\) is the alternating group from that of \(F_qA_5\).
Keywords:
Wedderburn decomposition, group algebra, 20C05
@article{SMJ2_2021_46_3_a3,
author = {Mittal, Gaurav and Sharma, Rajendra Kumar},
title = {When the {Wedderburn} decomposition of the semisimple group algebra {FqG} implies that of {Fq(G} {\texttimes} {C2)?}},
journal = {Serdica Mathematical Journal},
pages = {253--260},
year = {2021},
volume = {46},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SMJ2_2021_46_3_a3/}
}
TY - JOUR AU - Mittal, Gaurav AU - Sharma, Rajendra Kumar TI - When the Wedderburn decomposition of the semisimple group algebra FqG implies that of Fq(G × C2)? JO - Serdica Mathematical Journal PY - 2021 SP - 253 EP - 260 VL - 46 IS - 3 UR - http://geodesic.mathdoc.fr/item/SMJ2_2021_46_3_a3/ LA - en ID - SMJ2_2021_46_3_a3 ER -
%0 Journal Article %A Mittal, Gaurav %A Sharma, Rajendra Kumar %T When the Wedderburn decomposition of the semisimple group algebra FqG implies that of Fq(G × C2)? %J Serdica Mathematical Journal %D 2021 %P 253-260 %V 46 %N 3 %U http://geodesic.mathdoc.fr/item/SMJ2_2021_46_3_a3/ %G en %F SMJ2_2021_46_3_a3
Mittal, Gaurav; Sharma, Rajendra Kumar. When the Wedderburn decomposition of the semisimple group algebra FqG implies that of Fq(G × C2)?. Serdica Mathematical Journal, Tome 46 (2021) no. 3, pp. 253-260. http://geodesic.mathdoc.fr/item/SMJ2_2021_46_3_a3/