The solvable subgroups of large order of L2(p) , p≥5
DOI:
https://doi.org/10.24297/jam.v13i5.6578Keywords:
Maximal subgroup, solvable, p-nilpotent, formationAbstract
By using the following theoretical and computational algorithms , we determined the solvable subgroups of large order of the finite non-abelian simple linear groups G = L2(p) = PSL(2,p) , for p≥5 and p is a prime number , also their presentations and permutation representations have been found .
Downloads
Download data is not yet available.
References
1) Abdoly, V. D. ," An algorithm to construct representations of finite groups " , Ph.D thesis, Carleton University, 2003.
2) adams,J., " Character tables of GL(2) , SL(2) , PGL(2) and PSL(2) over a finite field",math.umd.edu,april2002.
www2.math.umd.edu/~jda/characters/characters.pdf3)
3) Breuer,T., " Solvable Subgroups of Maximal Order in Sporadic Simple Groups" , LehrstuhlDfurMathematikRWTH, 52056 Aachen, Germany, version(1) in 2006 and version(2) in 2012 .
www.math.rwth-aachen.de/ ~Thomas.Breuer/ctbllib/doc/sporsolv.pdf.
4) Breuer ,T. , " The GAP Character Table Library ", Version 1.2,2012 .
www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib 2012, GAP package.
5) Burnside,W. ," Theory of groups of finite order" . Dover Publications Inc., New York, 1955.
6) Connon ,J. ,Mckay,j. and Young,Kiang-Chuen , " The non-abelian simple groups G , |G| < 105 " , Communications in Algebra,Volume 7, Issue 13, pages 1397-1406 ,1979.
7) Cameron P. J. , Maimani H. R. , Omidi G. R. and Tayfeh-Rezaie B. , †3-designs from PSL(2,q) †, Elsevier Science , 2004
8) Dickson ,L. E., " Linear groups with an exposition of the Galois field theory ", Dover Publications Inc., New York, 1958.
9) Dixon,John D. , " Constructing representations of finite groups " , Groups and computation (New Brunswick, NJ, 1991) .
10) Dornhoff , L., " Group Representation Theory " , (Part A). Marcel Denker, 1971.
11) Drozd ,Yu.A. and Skuratovskii, R.v.," Generators and relations for products " , Ukrainian Mathematical Journal ,Volume 60, Number 7 (2008)
12) Giudici,M.,"Maximal subgroups of almost simple groups with socle PSL(2, q)" ,School of Mathematics and StatisticsThe University of Western Australia 35 Stirling Highway Crawley, Australia,2009. http://arxiv.org/pdf/math/0703685.pdf
13) Gorenstein ,D., " Finite Groups " ,Harper & Row New York, Evanston and London, Harper's Series in Modern Mathematics, 1968.
14) Gorenstein ,D., " The classification of finite simple groups " ,Vol. 1, journal of Groups, 1983.
15) Grove,L. C., " Groups and Characters" , John Wiley & Sons, New York, 1997.
16) Hall, Marshall Jr., " Simple groups of order less than one million " , Journal of Algebra 20: 98–102, 1972.
17) Issacs, I.M. ," Character Theory Of Finite Groups " , Dover Books on Mathematics , 1994.
18) James,G. and Liebeck, M., " Representations and characters of groups " , Cambridge Mathematical Textbooks, Cambridge University Press , Cambridge, 1993.
19) Mann, A. , " Soluble subgroups of symmetric and alternating groups " ,Israel Journal of Mathematics , Volume 55, Number 2, 1986.
20) Nickerson,S. J., " An Atlas of Characteristic Zero Representations " , Ph.D Thesis , University of Birmingham , 2006.
21) Rose, H.E. , " A Course on Finite Groups " , Springer London Dordrecht Heidelberg ,New York, 2000.
22) Vdovin, E. P. , " Abelian and Nilpotent Subgroups of Maximal Orders of Finite Simple Groups " , Ph.d thesis SB RAS, Institute of Mathematics ,2000.
23) WilsonR. , Walsh P., Tripp J., Suleiman, I., Rogers ,S.,Parker ,R., Norton ,S., Nickerson ,S ., Linton ,S., Bray ,J. and Abbott,R.,Conway,J.H. , Curtis, R.T., and Parker, R.A. " Atlas of Finite Group Representations",version(2) 1985 , version(3),2004-2012,Available online at : web.mat.bham.ac.uk/atlas/.
24) The GAP computational System , {Groups, Algorithms, and Programming}, Version 4.5, 2010 .(http://www.gap-system.org)
2) adams,J., " Character tables of GL(2) , SL(2) , PGL(2) and PSL(2) over a finite field",math.umd.edu,april2002.
www2.math.umd.edu/~jda/characters/characters.pdf3)
3) Breuer,T., " Solvable Subgroups of Maximal Order in Sporadic Simple Groups" , LehrstuhlDfurMathematikRWTH, 52056 Aachen, Germany, version(1) in 2006 and version(2) in 2012 .
www.math.rwth-aachen.de/ ~Thomas.Breuer/ctbllib/doc/sporsolv.pdf.
4) Breuer ,T. , " The GAP Character Table Library ", Version 1.2,2012 .
www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib 2012, GAP package.
5) Burnside,W. ," Theory of groups of finite order" . Dover Publications Inc., New York, 1955.
6) Connon ,J. ,Mckay,j. and Young,Kiang-Chuen , " The non-abelian simple groups G , |G| < 105 " , Communications in Algebra,Volume 7, Issue 13, pages 1397-1406 ,1979.
7) Cameron P. J. , Maimani H. R. , Omidi G. R. and Tayfeh-Rezaie B. , †3-designs from PSL(2,q) †, Elsevier Science , 2004
8) Dickson ,L. E., " Linear groups with an exposition of the Galois field theory ", Dover Publications Inc., New York, 1958.
9) Dixon,John D. , " Constructing representations of finite groups " , Groups and computation (New Brunswick, NJ, 1991) .
10) Dornhoff , L., " Group Representation Theory " , (Part A). Marcel Denker, 1971.
11) Drozd ,Yu.A. and Skuratovskii, R.v.," Generators and relations for products " , Ukrainian Mathematical Journal ,Volume 60, Number 7 (2008)
12) Giudici,M.,"Maximal subgroups of almost simple groups with socle PSL(2, q)" ,School of Mathematics and StatisticsThe University of Western Australia 35 Stirling Highway Crawley, Australia,2009. http://arxiv.org/pdf/math/0703685.pdf
13) Gorenstein ,D., " Finite Groups " ,Harper & Row New York, Evanston and London, Harper's Series in Modern Mathematics, 1968.
14) Gorenstein ,D., " The classification of finite simple groups " ,Vol. 1, journal of Groups, 1983.
15) Grove,L. C., " Groups and Characters" , John Wiley & Sons, New York, 1997.
16) Hall, Marshall Jr., " Simple groups of order less than one million " , Journal of Algebra 20: 98–102, 1972.
17) Issacs, I.M. ," Character Theory Of Finite Groups " , Dover Books on Mathematics , 1994.
18) James,G. and Liebeck, M., " Representations and characters of groups " , Cambridge Mathematical Textbooks, Cambridge University Press , Cambridge, 1993.
19) Mann, A. , " Soluble subgroups of symmetric and alternating groups " ,Israel Journal of Mathematics , Volume 55, Number 2, 1986.
20) Nickerson,S. J., " An Atlas of Characteristic Zero Representations " , Ph.D Thesis , University of Birmingham , 2006.
21) Rose, H.E. , " A Course on Finite Groups " , Springer London Dordrecht Heidelberg ,New York, 2000.
22) Vdovin, E. P. , " Abelian and Nilpotent Subgroups of Maximal Orders of Finite Simple Groups " , Ph.d thesis SB RAS, Institute of Mathematics ,2000.
23) WilsonR. , Walsh P., Tripp J., Suleiman, I., Rogers ,S.,Parker ,R., Norton ,S., Nickerson ,S ., Linton ,S., Bray ,J. and Abbott,R.,Conway,J.H. , Curtis, R.T., and Parker, R.A. " Atlas of Finite Group Representations",version(2) 1985 , version(3),2004-2012,Available online at : web.mat.bham.ac.uk/atlas/.
24) The GAP computational System , {Groups, Algorithms, and Programming}, Version 4.5, 2010 .(http://www.gap-system.org)
Downloads
Published
2017-12-27
How to Cite
Abduh, A. A., & AlGhawazi, A. A. (2017). The solvable subgroups of large order of L2(p) , p≥5. JOURNAL OF ADVANCES IN MATHEMATICS, 13(5), 7408–7415. https://doi.org/10.24297/jam.v13i5.6578
Issue
Section
Articles
License
All articles published in Journal of Advances in Linguistics are licensed under a Creative Commons Attribution 4.0 International License.
