For each binary operation * defined on a set below, determine whether or not * gives a group structure on the set. If it is a group, explain why it is a group. If it is not a group, say which axioms fail to hold: (a) Define * on Z by a * b max(a, b). %3D (b) Define * on Q \ {0} by a * b = |ab|. (c) Define * on Q+ by a * b = ab.

For each binary operation * defined on a set below, determine whether or not * gives a group structure on the set. If it is a group, explain why it is a group. If it is not a group, say which axioms fail to hold: (a) Define * on Z by a * b max(a, b). %3D (b) Define * on Q \ {0} by a * b = |ab|. (c) Define * on Q+ by a * b = ab.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.1: Definition Of A Group

Problem 31E

See similar textbooks