内容节选自 from J. Rotman’s Galois Theory - Appendix 1. 仅供学习时备忘使用.
Abelian Group. A group in which multiplication is commutative.
Alternating Group AnAn. The subgroup of SnSn consisting of all the even permutations. it has order 12n!12n!.
Associativity. For all x,y,zx,y,z, one has (xy)z=x(yz)(xy)z=x(yz). it follows that one does not need parentheses for any product of three or more factors.
Automorphism. An isomorphism of a group with itself.
Commutativity. For all x,yx,y, one has xy=yxxy=yx.