HallHigman type theorems. II
Author:
T. R. Berger
Journal:
Trans. Amer. Math. Soc. 205 (1975), 4769
MSC:
Primary 20C05
MathSciNet review:
0399229
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Abstract 
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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.
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, HallHigman type theorems. VIII, Proc. London Math. Soc. (to appear).
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Thomas
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solvable groups, Math. Z. 131 (1973), 305–312.
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order, J. Algebra 39 (1976), no. 1,
199–207. MR 0396729
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 [8]
T.
R. Berger, Primitive solvable groups, J. Algebra
33 (1975), 9–21. MR 0360806
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T. R. Berger and F. Gross, length and the derived length of a Sylow subgroup, Proc. London. Math. Soc. (to appear).
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Hall and Graham
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 [1]
 T. R. Berger, Automorphisms of solvable groups, J. Algebra 27 (1973), 311340. MR 0347978 (50:476)
 [2]
 , HallHigman type theorems. I, Canad. J. Math. 26 (1974), 513531. MR 0399228 (53:3079)
 [3]
 , HallHigman type theorems. III, Trans. Amer. Math. Soc. (to appear). MR 0437627 (55:10551)
 [4]
 , HallHigman type theorems. V, Pacific J. Math. (to appear). MR 482784 (81g:20008a)
 [5]
 , HallHigman type theorems. VIII, Proc. London Math. Soc. (to appear).
 [6]
 , Nilpotent fixed point free automorphisms groups of solvable groups, Math. Z. 131 (1973), 305312. 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), 921. 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), 142. MR 17, 344. MR 0072872 (17:344b)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197503992290
PII:
S 00029947(1975)03992290
Keywords:
HallHigman Theorem B,
representation theory,
group theory,
minimal module,
symplectic primitive module
Article copyright:
© Copyright 1975
American Mathematical Society
