COSETS AND LAGRANGES THEOREM
KEITH CONRAD
1. Introduction
Pick an integer m = 0. For a Z, the congruence class a mod m is the set of integers
a + mk as k runs over Z. We can write this set as a + mZ. This can be thought of as a
translated subgroup: start

Paper Code: MATH310-13B (HAM)
2013 B SEMESTER EXAMINATIONS
DEPARTM ENT Mathematics.
PAPER TITLE Modern Algebra.
Three hours. THE UNIVERSITY or
WAIKATO
NUMBER OF QUESTIONS Twelve.
IN EXAMINATION PAPER
NUMBER OF QUESTIONS
TO BE ANSWERED
VALUE OF EACH QU

MATH310-13B Test 2 (Group Theory)
1. Consider the following elements of 87.
a = (135) [3 = (1234)
(3) Compute aﬂ and ﬂex.
(b) Compute a‘1 and ﬂ”1.
(C) Write or and B as products of 2—cycles and identify them as even or odd.
(d) Compute the orders Ial and