The imprimitive subgroups GL(3,3)
Keywords:
Imprimitive, generated, presentation
Abstract
In this paper we determine the imprimitive subgroups of GL(3,3)
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References
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Bull.New York Math.soc.2 , 250-258.
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theory Leipzig.Reprinted by Dover New York 1958.
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15-John.D.Dixon and Brian Mortimer(1996) , Permutation Groups, springer-verlag
New York Berlin Heidelberg.
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less than 1000” Math.proc.comb.philos.soc.103 213-238.
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 GLn (2)
with n 6n ”, G.R.Math.Rep.Acad.Sci.Canada 1 , 75-78.
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incomputational Group Theory ed.Michael D.Atkinson Academic press London pp.367-
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Heidelberg
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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.
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27-C.Jordan(1917), ”Memoire sur less groups resolubles” , J.de Math.(7)3, 263.374.
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pergamon press, oxford, pp.47-57.
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
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32-A.S.Kondrat’ev(1985), ”Irreducible subgroups of the group GL(7,2) ” , Mat.Zametki 37
317-321.
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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 groupGL8 (2) ” , 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36-L.G.Kovacs , J.Neubuser and M.F.Newman(unpublished notes), ”some algorithms for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” , Amer.J.Math.26, 45-102.
39-Arne Ledet(1996) , subgroups of Hol(Q8) as Galios Groups, J.Algebra 181 , 478-506.
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, 13-17.
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.
43-E.Mathieu(1858) , C.R.Acad.sci:46 , 1048-1208.
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” , Bull.Amer.Math.soc.(2)5 ,
249-251.
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 n51,64 ”, in Eighth
All-Union Symposium on Group theory Abstracts of Reports Institue of Mathematices
Academy of scineces of the UkrSSR , Kiev, p.98.
55-B.A.Pogorelov(1980) , ”primitive permutation groups of low degree” , Algebra and logic
19 230-254 278-296.
56- B. Razzaghmaneshi, Determination of the JS-maximal of GL(n, pk). Ph.D Theses, 2002,
IUH university
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 J.canon(1984) , ”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.
7-A.L.Cauchy(1845) , C.R.Acad.sci.21 , 1363-1369.
8-A.Cayley(1891) , ”On the substitution groups for two , three, four, five, six, seven and eight
letters" Quart.j.pure Appl.Math.25 71-88 137-155.9-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 573 , springer-verlag, Berlin , Heidelberg,
pp.17-50.
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 GLn (q) ,
J.sci.uni.Tehran.VOL1(1996) 69-75.
13-Leonard Eugene Dikson(1901) , Linear Groups whith an Exposition of the Galios Field
theory Leipzig.Reprinted by Dover New York 1958.
14-John.D.Dixon(1971), The structure of linear Groups, Van Nostrand Reinhold, London.
15-John.D.Dixon and Brian Mortimer(1996) , Permutation Groups, springer-verlag
New York Berlin Heidelberg.
16-John.D.Dixon and Brian Mortimer(1988) , ”The primitive permutation groups of degree
less than 1000” Math.proc.comb.philos.soc.103 213-238.
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 GLn (2)
with n 6n ”, G.R.Math.Rep.Acad.Sci.Canada 1 , 75-78.
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 , Heidelberg.
23-B.Huppert and N.Blackburn(1982) , Finite Groups , Springer-verlag, 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 86(1964) , 98-128.
27-C.Jordan(1917), ”Memoire sur less groups resolubles” , J.de Math.(7)3, 263.374.
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 press, oxford, pp.47-57.
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 groupGL8 (2) ” , 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” , Amer.J.Math.26, 45-102.
39-Arne Ledet(1996) , subgroups of Hol(Q8) as Galios Groups, J.Algebra 181 , 478-506.
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, 13-17.
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.
43-E.Mathieu(1858) , C.R.Acad.sci:46 , 1048-1208.
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” , Bull.Amer.Math.soc.(2)5 ,
249-251.
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 n51,64 ”, in Eighth
All-Union Symposium on Group theory Abstracts of Reports Institue of Mathematices
Academy of scineces of the UkrSSR , Kiev, p.98.
55-B.A.Pogorelov(1980) , ”primitive permutation groups of low degree” , Algebra and logic
19 230-254 278-296.
56- B. Razzaghmaneshi, Determination of the JS-maximal of GL(n, pk). Ph.D Theses, 2002,
IUH university
Published
2018-08-30
How to Cite
Razzaghmaneshi, B. (2018). The imprimitive subgroups GL(3,3). GPH-International Journal of Mathematics, 1(1), 12-19. Retrieved from https://gphjournal.org/index.php/m/article/view/91
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