Geodesic
Hall Higman Type Theorems, I
Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 513-531

Voir la notice de l'article provenant de la source Cambridge University Press

Suppose Q is a q-group for a prime q and C ≦ Aut(Q) is cyclic of order pe for a prime p ≠ q. Let k be a splitting field for CQ, the semidirect product of C by Q, of characteristic r ≠ q. Let V be a faithful irreducible k[CQ]-module. The k[CQ]-module V has been widely studied. When r = p the situation outlined above is similar to the situation occurring in the proof of Theorem B of Hall and Higman [3]. When r ≠ p it is similar to the corresponding theorem of Shult [5]. In all but restricted cases V|C has a regular k[C]-direct summand. 
Berger, T. R. Hall Higman Type Theorems, I. Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 513-531. doi: 10.4153/CJM-1974-048-5
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[1] 1. Berger, T. R., Class two p-groups as fixed point free automorphism groups, Illinois. J. Math. 14 (1970), 121–149. Google Scholar

[2] 2. Gorenstein, D., Finite groups (Harper and Row, New York, 1968). Google Scholar

[3] 3. Hall, P. and Higman, G., On the p-length of p-s oh able groups and reduction theorems for Burnside's problem, Proc. London Math. Soc. 6 (1956), 1–42. Google Scholar

[4] 4. Passman, D. S., Solvable half-transitive automorphism groups, J. Algebra 6 (1967), 285–304. Google Scholar

[5] 5. Shult, E., On groups admitting fixed point free abelian operator groups, Illinois J. Math. 9 (1965), 701–720. Google Scholar

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