Elementary Abstract Algebra- Examples and Applications, 2019a

CONTENTS 11
id,e: Identity element of a group
( )
1 2 ... n
: Permutation in tableau format
a 1 a 2 ... a n
(a 1 ···a n1 )(b 1 ···b n2 ) ...: Permutation in cycle notation
N, Z, Q, R, C: natural numbers (positive integers), integers, rationals,
real numbers, complex numbers
Q ∗ , R ∗ , C ∗ : rationals, real numbers, complex numbers without 0
Z n :
Q 8 :
Integers mod n
Quaternion group ({±1, ±i, ±j, ±j ± k})
M n (Z, R, C ...):
Z[x], R[x],...:
n × n matrices with entries in Z,R,C....
Polynomials with coefficients in Z, R,....
GL n (R): General linear group of invertible n × n matrices with
coefficients in R.
U(n):
n.
Group of units (elements with multiplicative inverses) mod