Finite Simple Groups

Text Book: - Contemporary Abstract Algebra, Author:- Gallien In page 424 : - Theorem 25.1( Please mention each and every step). In page 424:- Theorem 25.2 (Please mention each and every step). Page 425 : - Theorem 25.3 (Please mention each and every step). Page 426 :- Corollary 1 and Corollary 2 (Please mention each ...continues

Group Theory : Special Topics and Finite Simple Groups

Text Book: - Contemporary Abstract Algebra, Author:- Gallien In page number 430 & 431 , I need following questions to be answered 6, 7, 8, 16 & 17. Last Question:- Give examples of groups with specific properties (Simple group & Non Simple Groups) At least 10 examples. (Please refer Chapter 25).? Please mention each ...continues

Group Theory : Generators and Relations

Text Book:- Contemporary Abstract Algebra. Author:- Gallien In page number 449, i need following questions to be answered: 4, 12/a, b, 21, 22, 24. 25. Please mention each and ever step.

Cayley Digraph

Can you graph this Cayley Digraph in the attachment?

Groups : Centralizers

For a fixed element a of a group G, the set Ca ={ x element-of G|ax=xa} is the centralizer of a in G. Prove that for any a element-of G, Ca is a subgroup of G.

Is the Set a Group?

Decide whether each of the given sets is a group with respect to the indicated operation. 1- For a fixed positive integer n, the set of all complex numbers x such that x^n=1(that is, the set of all nth roots of 1),with operation multiplication. 2-The set of all complex numbers x that have absolute value 1, with operation m ...continues

Finite Groups of Even Order

Suppose G is a finite group of even order. Show that there is at least one element a in G, a (is not equal to) e, such that a=a^-1

Maximum Revenue

The manager of a bicycle shop has found that, a a price (in dollars) of p(x) = 150 - x/4 per bicycle, x bicycles will be sold. a.find an expression for the total revenue from the sale of x bicycles. b.find the number of bicycle sales that leads to maximum revenue. c.find the maximum revenue.

Measure the height of a stack of 50 pennies (in centimeters).

1. Measure the height of a stack of 50 pennies (in centimeters). 2.Convert the height of the stack of pennies into meters 3.Calculate how many pennies would be needed to make a tower 1 billion meters tall. Give answer in both standard calculation and in scientific notation.

Group Theory, Computing number of odd order subgroups

Question: Let G be a group of order 2k , that contains a cyclic subgroup of order k, where k is odd. Determine a formula to compute the number of subgroups of G that are of odd order.