MATH 113 Study Guide - Midterm Guide: Coset, Abelian Group, Non-Abelian Group
Document Summary
Attempt to answer all of the following five questions. You do not need to justify your response to the true/false problems: this is a closed book exam. Please put away all your notes, textbooks, calculators and portable electronic devices and turn your mobile phones to silent" (non-vibrate) mode: explain your answers clearly and neatly, and in complete english sentences. State all theorems you have used from class. 1: (20 points) (a) let h be a subgroup of a group g . 2: true/false (20 points - 2 points each). 4: (25 points) (a) prove that z/7z z/7z is not isomorphic to z/49z. (b) let a be an abelian group of order 392. List all possible isomorphism classes of a. (c) assume further that a contains an element of order 196. List the possible isomorphism classes of a. (d) let g = z/49z z/4z z/2z. Find subgroups h, k g of order 2 such that g /h and.
