The Structure of Groups GL(3,F)
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Author(s)
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. |