MTH 421 Study Guide - Midterm Guide: Abelian Group, Multiple Choice, Positive Element
Document Summary
Direct products cyclic: let ( g, *) be a group and a in g. the order of a is the least positive integer n such that a^n = e. Direct products nontrivial subgroup: let (g, ) be a group. (g, ) is a cyclic if there is some a in g such that = g. Direct products nontrivial subgroup cyclic multiplication notation: let h be a nontrivial subgroup of (z, +). Then h is cyclic and is generated by its least positive element (gcd) cyclic multiplication notation addition notation nontrivial subgroup: n(a+b) = na + nb (ab) ^ n = a^n b^n. Cyclic subgroups addition notation: if (g1, ) and (g2, ) are groups, then their direct product is the cartesian product g1 x g2 with the operation defined by (a, b) (a1, b1) = (a a1, bb1). 9 multiple choice questions: let (g, *) be a group and a exist in g. define.
