Conjugacy Class Representatives for Group GL(q,F)

Abstract -- In this paper we show that a complete and irredundant set of
GL(q,F)–conjugacy class representatives of the primitive

Keywords -- irredundant set, conjugacy class, representatives

References --

1-Beverley Bolt,T.G.Room and G.E.Wall(1961-62), ”on the clifford collineation, transform and similarity groups.I and II”.j.Aust.Mast.soc.2,60-96.
2-W.Burnside(1897),Theory of Groups of Finite Order, 1stedn.Combridge univercity press.
3-W.Burnside(1911),Theory of Groups of Finite Order,2nd edn, Combridge univercity press.Reprinted by Dover,New York,1955.
4-Gregory Buttler and John Mckay(1983), ”The transitive groups of degree up to eleven" ,comm.Algebra 11,863-911.
5-John, ”An introduction to the group theory language,cayley" ,in computaional Group Theory,ed.Michael D.Atkinson,Academic press,London,pp.145-183.
6-Jhon canon(1987), ”The subgroup lattice module" ,in the CAYLEY
Bulletin, no.3, ed.John canon,department of pure Mathematics,
Univercity of sydney,pp.42-69.
8-A.Cayley(1891), ”On the substitution groups for two,three,four,
five,six,seven and eight letters" ,Quart.j.pure Appl.Math.25,71-88,
9-F.N.Cole(1893b), ”The transitive substitution-groups of nine
letters” ,
Bull.New York Math.soc.2,250-258.
10-S.B.Conlon(1977), ”Nonabelian subgroups of prime-power order of
classical groups of the same prime degree, ”In group theory ,eds
R.A.Bryce,J.coosey and M.F.Newman,lecture Notes in Mathematics
11-J.H.Conway,R.T.Curtis,S.P.Norton,R.A.Parker and
R.A.Wilson(1985),Atlas of Finite Groups,clarendon press,oxford.
12-M.R.Darafsheh,On a permutation character of the Group GL (q) n ,
13-Leonard Eugene Dikson(1901),Linear Groups whith an Exposition
of the Galios Field theory,Leipzig.Reprinted by Dover,New York,
14-John.D.Dixon(1971),The structure of linear Groups,Van Nostrand
Reinhold, London.
15-John.D.Dixon and Brian Mortimer(1996),Permutation Groups,
New York Berlin Heidelberg.
16-John.D.Dixon and Brian Mortimer(1988), ”The primitive
permutation groups of degree less than 1000” ,
17-Volkmar Felsch and Gunter sandlobes(1984), ”An interactive
program for computing subgroups”.In Computational Group Theory,
ed.Michael D.Atkinson,Academic press,London,pp.137-143.
18-Fletcher Gross(to appear), ”On the uniqueness of wreath
products” ,J.Algebra.
19-Koichiro Harada and Hiroyoshi Yamaki(1979), ”The irreducible
subgroups of (2) n GL with n n  6 ” ,G.R.Math.Rep.Acad.Sci.Canada 1,75-
20-George Havas and L.G.Kovacs(1984), ”Distinguishing eleven
crossing Konts” ,incomputational Group Theory ,ed.Michael
D.Atkinson,Academic press, London, pp.367-373.
21-Derek F.Holt and W.plesken(1989),Perfect Groups,oxford
university press, Oxford.
22-B.Huppert(1967),Endliche Gruppen I,springer-verlag,Berlin,
23-B.Huppert and N.Blackburn(1982),Finite Groups  ,Springerverlag,
berlin, Heidelberg.
24-I.Il’in and A.S.Takmakov(1986) , ”Primitive simple permutation
groups of small degress” ,Algebra and logic 25,167-171.
25-I.M.Isaucs(1975), ”Character degrees and derived length of a
solvable group” Canad.J.Math.27,146-151.
26-L.M.Isaucs,characters of  separable groups,j.Algebra
27-C.Jordan(1917), ”Memoire sur less groups resolubles” ,
28-C.Jordan(1974), ”Sur deux points de la theorie des
substitution” , C.R.Acad.sci.79,1149-1151.
29-C.Jordan(1971b), ”Sur la classification des groups primitives” ,
C.R.A cad.sci.73,853-857.
30-H.Jurgensen(1970), ”Calculation with the elements of a finite
group given by generators and defining relations” ,in
computational problem sin Abstract Algebra,ed.John leech,pergamon
31-T.P.Kirkman(1862-3), ”The complete theory of group,being the
solution of the mathematical prize question of the French
Academy for 1860” ,proc.Manchester Lit.philos.soc.3,133-152,161-
162.Erratum:ibid.4(1865) ,171-172.
32-A.S.Kondrat’ev(1985) , ”Irreducible subgroups of the group
GL(7,2) ” , Mat.Zametki 37,317-321.
33-A.S.Kondrat’ev(1986a) , ”Irreducible subgroups of the group
GL(9,2) ” , Mat.Zametki 39,320-329.
34-A.S.Kondratev(1986b), ”linear groups of small degree over a
field of order 2” ,(Russian),Algebra I Logika 25,544-565.
35-A.S.Kondratev(1987), ”The irreducible subgroups of the group
(2) 8 GL ” , comm.Algebra 15,1039-1093.
36-L.G.Kovacs,J.Neubuser and M.F.Newman(unpublished notes), ”some
algorithms for finite soluble groups” ,.
37-L.G.Kovacs(1986),Maximal subgroups in Composite Finite Groups,
J.Algebra 99,114-131.
38-H.W.Kuhu(1904), ”On impritive substitution groups” ,
39-Arne Ledet(1996),subgroups of ( ) 8 Hol Q as Galios Groups,J.Algebra
40-Martin W.Liebeck,cheryl E.Preeger and Jan Saxl(1988), ”On the
O'Nan scott theorem for finite primitive permutation groups” ,
J.Austral.Math.soc.(series A)44,389-396.
41-G.Liskovec(1973), ”Maximal biprimary permutation groups” ,
(Russian),Vesci Akad. Navuk BSSR ser.Fi z.Math.Navuk 1973,no.6,13-
42-E.N.Martin(1901), ”On the imprimitive substituation groups of
degree fifteen and the primitive substitutation groups of degree
eighteen” ,Amer.J.Math.23,259-286.
44-G.A.Miller(1894b), ”Note on the substitution groups of eight
and nine letters” ,Bull.New york Math.soc.3,242-245.
45-G.A.Miller(1898b), ”on the primitive substitution groups of
degree sixteen” , Amer.J.Math.20,229-241.
46-G.A.Miller(1895c), ”Note on the transitive substitution groups
of degree twelve” , Bull.Amer.Math.soc.(2)1,255-258.
47-G.A.Miller(1899), ”Note on Burnside’s theory of Groups” ,
48-G.A.Miller(1900), ”0n the transitive substitution groups of
degree seventeen” ,Quart.J.Pure Appl.Math.31,49-47.
49-G.A.Miller(1900b), ”On the primitive substitution groups of
degree ten” , Quart.J.Pure Appl.Math.31,228-233.
50-M.F.Newman(1976), ”calculating presentations for certain kinde
of quotinet groups” , SYMSAG’76 ,Association for computing Machinery
,New York,pp.2-8.
51-M.F.Newman and E.A.O'Brien(1989), ”A CAYLEY library for the
groups of order dividing 128” ,in Group theory,eds K.N.cheng and
Y.K.Leong,Walter de Gruyter, Berlin,New York,pp.437-442.
52-W.Nickel,A.Niemeyer and M.Schonert(1988) ,GAP Getting started
and refrence manual,Lehrustuhl D fur Mathematik,RWTH Aachen.
53-W.Plesken(1987), ”To wards a soluble quotient algoritm” ,
J.symbolic comput.4, 111-122.
54-B.A.Pogorelov(1982), ”Primitive permutation groups of degree
n51,64 ” ,in Eighth All-Union Symposium on Group theory,Abstracts
of Reports,Institue of Mathematices,Academy of scineces of the
55-B.A.Pogorelov(1980), ”primitive permutation groups of low
degree” ,Algebra and logic 19,230-254,278-296.
56-Derek J.s.Robinson(1982),A course in the Theory of Groups,
springer verlag, New York.
57-Gordan F.Royal(1987), ”The transitive groups of degree twelve” ,
J.Symbolic comput.4,255-268.
58-M.Schaps(1968), ”An algorithm to generate subgroups of finite
index in a group given by defining relations” ,manuscript,Kiel.
59-J.A.Serret(1850), ”Memoire sur less functions de quatre,cing et
six lettre” , J.Math.pures Appl.(1)15,45-70.
60-Hyo-Seob Sim(1993),Degree of Irreducible Representations of
Metacyclic Groups,J.Comm.Algebra,21(10) ,3773-3777.
61-Charles C.Simss(1970), ”Computational methods in the study of
perm-utation groups” ,in computational problems in Abstract
Algebra,ed,John Leech,pergamon press,Oxford,pp.169-183.
62-M.Slattery,Pi -blocks of Pi -separable groups  ,j.Algebra
63-M.Slattery,Pi -blocks of Pi -separable groups  ,j.Algebra
64-M.W.Short(1992), ”The Primitive Soluble Permutation Groups of
Degree Less Than 256” ,Lecture Notes in Mathemaics,1519,springerverlag
Berlin Heidelberg New York.
65-D.A.Supruneko(1963),Soluble and Nilpotent Linear
Groups.Translation of Mathematical Monographs,vol.9,American
Mathematical society,providence,Rhode Island.
66-D.A.Suprunenko(1976),Matrix Group,Translation of Mathematical
Monographs,VOL.45,American Mathematical society,Provideence,Rhode
67-Michio Suzuki(1982),Group theory  ,Springer-verlag,New York.
68-Michio Suzuki(1986),Group theory  ,Springer-verlag,New York.
69-Tang Shou Wen and Wang Jie(1988, ”The primitive permutation
groups of degree 21 to 30” ,(Chinese),Beijing Daxue Xuebao 24,269-
70-William Hulme Wilson(1972), ”Primitive irreducible linear
groups” ,Msc the-sis, Australian National University.
71-David L.Winter(1972), ”The automorphism group of an
P-group” ,Rocky Mountain J.Math.2,159-168.
72-Olaf.Manz and Thomas R.Wolf(1993),Representations of Solvable
Groups, Cambridge University press.
73-T.R.Wolf,Solvable and nilpotent subgroups of ( , ), m GL n q
Can.j.Math.34(1982), 1097-1111.
74-T.R.Wolf,Sylow-P-subgroups of P-solvable subgroups of GL(n, p),
Archivder Math.43(1984),1-10.
75-T.R.Wolf,Character correspondences and  Special characters
in  Separable groups,can.j.Math.39(1987),920.937.
76-Hans J.Zassenhaus(1958),The Theory of Groups,2nd edu,chelsea
publishing company,New York.



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About the Author

Behnam Razzaghmaneshi

Assistant professor of Department of Mathematics
Talesh Branch, Islamic Azad University, Talesh, Iran

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