We prove that the mapping class group M (N-g) of a closed nonorientable surface of genus g different than 4 is generated by three torsion elements. Moreover, for every even integer k >= 12 and g of the form g = pk + 2q(k - 1) or g = pk + 2q(k - 1) + 1, where p, q are non-negative integers and p is odd, M (N-g) is generated by three conjugate elements of order k. Analogous results are proved for the subgroup of M (N-g) generated by Dehn twists.
机构:
South China Univ Technol, Sch Math, 381 Wushan Rd, Guangzhou 510630, Guangdong, Peoples R ChinaSouth China Univ Technol, Sch Math, 381 Wushan Rd, Guangzhou 510630, Guangdong, Peoples R China