四阶整数辛群中扭元的共轭类

Conjugacy Classes of Torsion in $4\times 4$ Integral Symplectic Group

中文关键词:  整数辛群  扭元  辛群空间  辛直和  准直和  回文多项式  辛补空间.

英文关键词:integral symplectic group  torsion  symplectic group space  symplectic direct sum  quasi-direct sum  palindromic monic polynomial  symplectic complement.

中文摘要:

      本文给出四阶整数辛群中扭元的全部共轭等价类.总共有55个不同的扭元等价类,它们的阶数分别是2, 3, 4, 5, 6, 8, 10, 12.没有其它阶的扭元.

英文摘要:

      A complete list of representatives of conjugacy classes of torsion in $4\times 4$ integral symplectic group is given in this paper. There are $55$ distinct such classes and each torsion element has order of $2,3,4,5,6,8,10$ and $12$.