--%>
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 : Problem on sales and budget XYZ Farm

    XYZ Farm Supply data regarding the store's operations follow: • Sales are budgeted at $480,000 for November, $430,000 for December, and $340,000 for January. • Collections are expected

    		•
  • Q : Maths assignment complete assignment

    complete assignment with clear solution and explanation

    		•
  • Q : The mean of the sampling distribution

    1. Caterer determines that 87% of people who sampled the food thought it was delicious. A random sample of 144 out of population of 5000 taken. The 144 are asked to sample the food. If P-hat is the proportion saying that the food is delicious, what is the mean of the sampling distribution p-hat?<

    		•
  • Q : Profit-loss based problems A leather

    A leather wholesaler supplies leather to shoe companies. The manufacturing quantity requirements of leather differ depending upon the amount of leather ordered by the shoe companies to him. Due to the volatility in orders, he is unable to precisely predict what will b

    		•
  • Q : Define terms Terms : Terms are defined

    Terms: Terms are defined inductively by the following clauses.               (i) Every individual variable and every individual constant is a term. (Such a term is called atom

    		•
  • Q : Nonlinear integer programming problem

    Explain Nonlinear integer programming problem with an example ?

    		•
  • Q : Who derived the Black–Scholes Equation

    Who derived the Black–Scholes Equation?

    		•
  • Q : What is the definition of a group Group

    Group: Let G be a set. When we say that o is a binary operation on G, we mean that o is a function from GxG into G. Informally, o takes pairs of elements of G as input and produces single elements of G as output. Examples are the operations + and x of

    		•
  • Q : Area Functions & Theorem Area Functions

    Area Functions 1. (a) Draw the line y = 2t + 1 and use geometry to find the area under this line, above the t - axis, and between the vertical lines t = 1 and t = 3. (b) If x > 1, let A(x) be the area of the region that lies under the line y = 2t + 1 between t

    		•
  • Q : Numerical Analysis Hi, I was wondering

    Hi, I was wondering if there is anyone who can perform numerical analysis and write a code when required. Thanks

    		•