|
Hurwitz groups: A brief survey
Author(s):
Marston
Conder
Journal:
Bull. Amer. Math. Soc.
23
(1990),
359-370.
MSC (1985):
Primary 20F05;
Secondary 57S25
MathSciNet review:
1041434
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- 1.
- A. F. Beardon, The geometry of discrete groups, Springer-Verlag, Berlin, 1980. MR 1393195
- 2.
- J. M. Cohen, On Hurwitz extensions byPSL2(7), Math. Proc. Cambridge Philos. Soc. 86 (1979), 395-400. MR 542684
- 3.
- J. M. Cohen, On non-Hurwitz groups and non-congruence subgroups of the modular group, Glasgow Math. J. 22 (1981), 1-7. MR 604811
- 4.
- M. D. E. Conder, Generators for alternating and symmetric groups, J. London Math. Soc. (2) 22 (1980), 75-86. MR 579811
- 5.
- M. D. E. Conder, A family of Hurwitz groups with non-trivial centres, Bull. Austral. Math. Soc. 33 (1986), 123-130. MR 823860
- 6.
- M. D. E. Conder, Hurwitz groups with arbitrarily large centres, Bull. London Math. Soc. 18 (1986), 269-271. MR 829585
- 7.
- M. D. E. Conder, The genus of compact Riemann surfaces with maximal automorphism group, J. Algebra 108 (1987), 204-247. MR 887205
- 8.
- M. D. E. Conder and J. McKay, A necessary condition for transitivity of a finite permutation group, Bull. London Math. Soc. 20 (1988), 235-238. MR 931183
- 9.
- H. S. M. Coxeter, The abstract groups G, Trans. Amer. Math. Soc. 45 (1939), 73-150. MR 1501984
- 10.
- H. S. M. Coxeter and W. O. J. Moser, Generators and relations for discrete groups, 4th ed., Springer-Verlag, Berlin, 1980. MR 562913
- 11.
- L. Finkelstein and A. Rudvalis, Maximal subgroups of the Hall-Janko-Wales group, J. Algebra 24 (1973), 486-493. MR 323889
- 12.
- D. Gorenstein, Finite groups, 2nd ed., Chelsea Publishing Company, New York, 1980. MR 569209
- 13.
- G. Higman, Construction of simple groups from character tables, Finite Simple Groups (M. B. Powell and G. Higman, eds.), Academic Press, New York, 1971, pp. 205-214. MR 342603
- 14.
- A. Hurwitz, Über algebraische Gebilde mit eindeutigen Transformationen in sich, Math. Ann. 41 (1893), 403-442. MR 1510753
- 15.
- G. A. Jones and D. Singerman, Complex functions: an algebraic and geometric viewpoint, Cambridge Univ. Press, 1987. MR 890746
- 16.
- P. B. Kleidman, R. A. Parker, and R. A. Wilson, The maximal subgroups of the Fischer groupFi23, J. London Math. Soc. (2) 39 (1989), 89-101. MR 989922
- 17.
- J. Leech and J. Mennicke, Note on a conjecture of Coxeter, Proc. Glasgow Math. Assoc. 5 (1961), 25-29. MR 150193
- 18.
- J. Leech, Generators for certain normal subgroups of (2, 3, 7), Proc. Cambridge Philos. Soc. 61 (1965), 321-332. MR 174621
- 19.
- J. Leech, Note on the abstract group (2, 3, 7; 9), Proc. Cambridge Philos. Soc. 62 (1966), 7-10. MR 190214
- 20.
- J. Lehner and M. Newman, On Riemann surfaces with maximal automorphism groups, Glasgow Math. J. 8 (1967), 102-112. MR 220924
- 21.
- J. Lehner, Lectures on modular forms, Appl. Math. Ser., vol. 61, U. S. National Bureau of Standards, Washington, D.C., 1969. MR 264070
- 22.
- S. A. Linton and R. A. Wilson, personal communication.
- 23.
- A. M. Macbeath, On a theorem of Hurwitz, Proc. Glasgow Math. Assoc. 5 (1961), 90-96. MR 146724
- 24.
- A. M. Macbeath, Generators of the linear fractional groups, Number Theory, Proc. Sympos. Pure Math., vol. XII, Amer. Math. Soc. Providence, R.I., 1969, pp. 14-32. MR 262379
- 25.
- J. Neubüser, H. Pahlings, and W. Plesken, CAS: Design and use of a system for the handling of characters of finite groups, Computational Group Theory (M. Atkinson, ed.), Academic Press, New York, 1984, pp. 195-247. MR 760658
- 26.
- G. Rosenberger, Von Untergruppen der Triangel-Gruppen, Illinois J. Math. 22(1978), 403-413. MR 497484
- 27.
- C.-H. Sah, Groups related to compact Riemann surfaces, Acta Math. 123 (1969), 13-42. MR 251216
- 28.
- D. Singerman, Automorphisms of compact non-orientable Riemann surfaces, Glasgow Math. J. 12 (1971), 50-59. MR 296286
- 29.
- A. Sinkov, On the group-defining relations (2, 3, 7; p), Ann. of Math. 38 (1937), 67-76.
- 30.
- A. J. Woldar, On Hurwitz generation and genus actions of sporadic groups, Illinois J. Math. 33 (1989), 416-437. MR 996351
- 31.
- A. J. Woldar, Sporadic simple groups which are Hurwitz, preprint. MR 1140615
- 32.
- M. F. Worboys, Generators for the sporadic group Co, Proc. Edinburgh Math. Soc. 25 (1982), 65-68. MR 648901
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1985):
20F05, 57S25
Retrieve articles in all Journals with MSC
(1985):
20F05, 57S25
Additional Information:
DOI:
10.1090/S0273-0979-1990-15933-6
PII:
S 0273-0979(1990)15933-6
|
Comments: webmaster@ams.org