Serial Group Rings of Finite Simple Groups of Lie Type

Suppose that F is a field whose characteristic p divides the order of a finite group G . It is shown that if G is one of the groups 3 D 4 ( q ), E 6 ( q ), 2 E 6 ( q ), E 7 ( q ), E 8 ( q ), F 4 ( q ), 2 F 4 ( q ), or 2 G 2 ( q ), then the group ring FG is not serial. If G = G 2 ( q 2 ), then the ri...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2018-09, Vol.233 (5), p.695-701
Main Authors: Kukharev, A. V., Puninski, G. E.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Rings (mathematics)
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Summary:Suppose that F is a field whose characteristic p divides the order of a finite group G . It is shown that if G is one of the groups 3 D 4 ( q ), E 6 ( q ), 2 E 6 ( q ), E 7 ( q ), E 8 ( q ), F 4 ( q ), 2 F 4 ( q ), or 2 G 2 ( q ), then the group ring FG is not serial. If G = G 2 ( q 2 ), then the ring FG is serial if and only if either p > 2 divides q 2 − 1, or p = 7 divides q 2 + 3 q + 1 but 49 does not divide this number.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-018-3957-z