--%>
Assignment Help - homework help

Examples of groups

Examples of groups: We now start to survey a wide range of examples of groups (labelled by (A), (B), (C), . . . ). Most of these come from number theory. In all cases, the group axioms should be checked. This is easy for almost all of the examples, and will be left as an exercise except in the occasional more difficult or subtle case.

(A) Our first examples are groups of numbers under addition. To begin, each of the sets Z (the integers), Q (the rational numbers), R (the real numbers) and C (the complex numbers) forms a group under the binary operation + of addition (exercise). Clearly, the groups are all abelian.

(B) For any fixed n ≡ Z, the set nZ = {na : a ≡ Z} is a subgroup of Z (exercise). A few speci fic cases are:

0Z = {0};
1Z = ( -1)Z = Z;
2Z = ( -2)Z = {2a : a ≡ Z}
= the set of even integers:

   Related Questions in Mathematics

  • Q : Maths A cricketer cn throw a ball to a

    A cricketer cn throw a ball to a max horizontl distnce of 100m. If he throws d same ball vertically upwards then the max height upto which he can throw is????

    		•
  • Q : Explain Black–Scholes model Explain

    Explain Black–Scholes model.

    		•
  • Q : Relationships Between Data Introduction

    Relationships Between Data - Introduction to Linear Regression Simple Regression Notes If you need guidance in terms of using Excel to run regressions, check pages 1 - 10 of the Excel - Linear Regression Tutorial posted to th

    		•
  • Q : Who developed a rigorous theory for

    Who developed a rigorous theory for Brownian motion?

    		•
  • Q : Mathematical and Theoretical Biology

    Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in the fields of biology, biotechnology, and medicine. The field may be referred to as mathematical biology or biomathematics to stress the mathematical

    		•
  • Q : Who had find Monte Carlo and finite

    Who had find Monte Carlo and finite differences of the binomial model?

    		•
  • Q : Set Theory & Model of a Boolean Algebra

    II. Prove that Set Theory is a Model of a Boolean Algebra The three Boolean operations of Set Theory are the three set operations of union (U), intersection (upside down U), and complement ~.  Addition is set

    		•
  • Q : Research Areas in Medical Mathematical

    Some Research Areas in Medical Mathematical Modelling:1. Modeling and numerical simulations of the nanometric aerosols in the lower portion of the bronchial tree. 2. Multiscale mathematical modeling of

    		•
  • Q : State Fermat algorithm The basic Fermat

    The basic Fermat algorithm is as follows: Assume that n is an odd positive integer. Set c = [√n] (`ceiling of √n '). Then we consider in turn the numbers c2 - n; (c+1)2 - n; (c+2)2 - n..... until a perfect square is found. If th

    		•
  • Q : What is Non-Logical Vocabulary

    Non-Logical Vocabulary: 1. Predicates, called also relation symbols, each with its associated arity. For our needs, we may assume that the number of predicates is finite. But this is not essential. We can have an infinite list of predicates, P

    		•