The Structure of Groups GL(3,F)

Volume 2, Issue 1, February 2017     |     PP. 1-14      |     PDF (634 K)    |     Pub. Date: February 27, 2017
DOI:    434 Downloads     8002 Views  

Author(s)

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

Abstract
Let be the JS-imprimitive of that is . This group has order 48 and is generated by the matrices... ...

Keywords
polycyclic presentation, imprimitive, conjugacy class

Cite this paper
Behnam Razzaghmaneshi, The Structure of Groups GL(3,F) , SCIREA Journal of Mathematics. Volume 2, Issue 1, February 2017 | PP. 1-14.

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 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 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 with ” 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 ” Mat.Zametki 37 317-321.
[ 33 ] A.S.Kondrat’ev(1986a) ”Irreducible subgroups of the group ” 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 ” 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 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) Vesc Akad. Navuk BSSR ser.F 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 ” 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 ] 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 P -blocks of P -separable groups j.Algebra 102(1986) 60-77.
[ 63 ] M.Slattery P -blocks of P -separable groups j.Algebra 124(1989) 236-269.
[ 64 ] M.W.Short(1992) ”The Primitive Soluble Permutation Groups of Degree Less Than 256” Lecture Notes in Mathemaics 1519 springer-verlag 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 Island.
[ 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 24 269-276.
[ 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 extraspecial 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 Can.j.Math.34(1982) 1097-1111.
[ 74 ] T.R.Wolf Sylow-P-subgroups of P-solvable subgroups of 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.