学习 Galois 理论须知的群论概念

学习 Galois 理论须知的群论概念

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.

阅读更多