Hall-Higman type theorems. II

Author:
T. R. Berger

Journal:
Trans. Amer. Math. Soc. **205** (1975), 47-69

MSC:
Primary 20C05

DOI:
https://doi.org/10.1090/S0002-9947-1975-0399229-0

MathSciNet review:
0399229

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Abstract: This paper continues the investigations of this series. Suppose GF is a field for a prime -is a nilpotent; is a nonsingular symplectic space with form ; and is a faithful irreducible -module where fixes the form . This paper describes completely the structure of and its representation upon when is symplectic primitive. This latter condition is described in §4 and is a primitivity condition.

**[1]**T. R. Berger,*Automorphisms of solvable groups*, J. Algebra**27**(1973), 311-340. MR**0347978 (50:476)****[2]**-,*Hall-Higman type theorems*. I, Canad. J. Math.**26**(1974), 513-531. MR**0399228 (53:3079)****[3]**-,*Hall-Higman type theorems*. III, Trans. Amer. Math. Soc. (to appear). MR**0437627 (55:10551)****[4]**-,*Hall-Higman type theorems*. V, Pacific J. Math. (to appear). MR**482784 (81g:20008a)****[5]**-,*Hall-Higman type theorems*. VIII, Proc. London Math. Soc. (to appear).**[6]**-,*Nilpotent fixed point free automorphisms groups of solvable groups*, Math. Z.**131**(1973), 305-312. MR**0338174 (49:2940)****[7]**T. R. Berger,*Characters and derived length in groups of odd order*, J. Algebra (to appear). MR**0396729 (53:590)****[8]**-,*Primitive solvable groups*, J. Algebra**33**(1975), 9-21. MR**0360806 (50:13253)****[9]**T. R. Berger and F. Gross,*-length and the derived length of a Sylow -subgroup*, Proc. London. Math. Soc. (to appear).**[10]**P. Hall and G. Higman,*On the -length of -soluble groups and reduction theorems for Burnside's problem*, Proc. London Math. Soc.**6**(1956), 1-42. MR**17**, 344. MR**0072872 (17:344b)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1975-0399229-0

Keywords:
Hall-Higman Theorem B,
representation theory,
group theory,
minimal module,
symplectic primitive module

Article copyright:
© Copyright 1975
American Mathematical Society