## Rocky Mountain Journal of Mathematics

### Real Genus Actions of Finite Simple Groups

Coy L. May

#### Article information

Source
Rocky Mountain J. Math., Volume 31, Number 2 (2001), 539-551.

Dates
First available in Project Euclid: 5 June 2007

https://projecteuclid.org/euclid.rmjm/1181070211

Digital Object Identifier
doi:10.1216/rmjm/1020171573

Mathematical Reviews number (MathSciNet)
MR1840952

Zentralblatt MATH identifier
0984.30026

#### Citation

May, Coy L. Real Genus Actions of Finite Simple Groups. Rocky Mountain J. Math. 31 (2001), no. 2, 539--551. doi:10.1216/rmjm/1020171573. https://projecteuclid.org/euclid.rmjm/1181070211

#### References

• N.L. Alling and N. Greenleaf, Foundations of the theory of Klein surfaces, Lecture Notes in Math. 219, Springer-Verlag, Berlin, 1971.
• E. Bujalance, J.J. Etayo, J.M. Gamboa and G. Gromadzki, Automorphism groups of compact bordered Klein surfaces, Lecture Notes in Math. 1439, Springer-Verlag, Berlin, 1990.
• M.D.E. Conder, Generators of the alternating and symmetric groups, J. London Math. Soc. (2) 22 (1980), 75-86.
• H.S.M. Coxeter, The abstract groups $G^m,n,p$, Trans. Amer. Math. Soc. 45 (1939), 73-150.
• H.S.M. Coxeter and W.O. Moser, Generators and relations for discrete groups, 4 -1957.
• D. Gorenstein, Finite groups, Harper and Row, New York, 1968.
• N. Greenleaf and C.L. May, Bordered Klein surfaces with maximal symmetry, Trans. Amer. Math. Soc. 274 (1982), 265-283.
• A.M. Macbeath, Generators of the linear fractional groups, in Number theory, Proc. Sympos. Pure Math. 12, Amer. Math. Soc., Providence, RI, 1969, 14-32.
• C.L. May, Automorphisms of compact Klein surfaces with boundary, Pacific J. Math. 59 (1975), 199-210.
• --------, Large automorphism groups of compact Klein surfaces with boundary, Glasgow Math. J. 18 (1977), 1-10.
• --------, The species of bordered Klein surfaces with maximal symmetry of low genus, Pacific J. Math. 111 (1984), 371-394.
• --------, Finite groups acting on bordered surfaces and the real genus of a group, Rocky Mountain J. Math. 23 (1993), 707-724.
• --------, The groups of real genus four, Michigan Math. J. 39 (1992), 219-228.
• --------, Finite metacyclic groups acting on bordered surfaces, Glasgow Math. J. 36 (1994), 233-240.
• --------, A lower bound for the real genus of a finite group, Canad. J. Math. 46 (1994), 1275-1286.
• --------, The groups of small real genus, Houston Math. J. 20 (1994), 393-408.
• --------, Finite $3$-groups acting on bordered surfaces, Glasgow Math. J. 40 (1998), 463-472.
• D. McCullough, Minimal genus of abelian actions on Klein surfaces with boundary, Math. Z. 205 (1990), 421-436.
• J.J. Rotman, The theory of groups, Allyn and Bacon, Boston, 1973.
• W.R. Scott, Group theory, Prentice-Hall, Englewood Cliffs, N.J., 1964.
• D. Singerman, $\psl(2,q)$ as an image of the extended modular group with applications to group actions on surfaces, Proc. Edinburgh Math. Soc. 30 (1987), 143-151.
• A.J. Woldar, Genus actions of finite simple groups, Illinois J. Math. 33 (1989), 438-450.