Purchase Solution

Abstract Algebra : Prove that if F is a Permutation on A

Not what you're looking for?

Ask Custom Question

A-Prove that if F is a permutation on A, then F^-1 is a permutation on A.

B-Prove that if F is a permutation on A, then (F^-1)^-1 = F

Purchase this Solution
Solution Summary

Permutations are investigated. The expert analyzes the abstract algebra.

Solution Preview

a permutation on A is a bijection from A to itself

if F is a permutation of A, F is a ...

Purchase this Solution
Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

View More Free Quizzes
Related BrainMass Solutions

  • Abstract Algebra: Groups

    86564 Abstract Algebra: Groups (See attached file for full problem description) 2.22 Define f: {0,1,2,...,10} {0,1,2,...,10} by f(n)= the remainder after dividing by 11. (I) Show that f is a permutation. (II) Compute the parity of f.

  • Group Theory : Permutation Groups

    88539 Group Theory : Permutation Groups Prove that there is no a such that a^( - 1 ) ( 1 , 2 , 3 ) a = ( 1 , 3 )( 5 , 7 , 8 ) Please see the attached file for the complete solution.

  • Permutation Groups

    This solution is comprised of a detailed explanation to prove that there exists subgroups Ni ( for some r) such that G = N0 > N1 >N2 >N3 > ... >Nr = (e) where Ni is a normal subgroup of Ni-1 and where Ni-1 /Ni is abelian.

  • Two questions in group theory

    172191 Two questions in group theory Problem #1 Prove that Aut(V)= (S3)and that Aut(S3)= S3. Problem #2 If H and K are normal subgroups of a group G with HK = G.

  • Permutation Groups

    88891 Group Theory : Permutation Groups Prove that the smallest subgroup of Sn containing ( 1 , 2 )and ( 1 , 2 , ... , n ) is Sn. ( In other words, these generate Sn ) Please see the attached file for the complete solution.

  • Counting Principle: Permutation Groups

    Another Counting Principle Using the theorem ' If O(G) = p^n , where p is a prime number, then Z(G) ≠ (e) ' as a tool, prove that if O(G) = p^n where p is a prime number, then G has a subgroup

  • Group Theory : Permutation Groups and Counting Principles

    89844 Group Theory : Permutaion Groups and Counting Principles Using O(N) = Σca for some choices of a in N , prove that in A5 there is no normal subgroup N other than (e) and A5 . Please see the attached file for the complete solution.

  • Group Theory : If in a finite group G an element a has exactly two conjugates, prove that G has a normal subgroup N ≠ e , G.

    89473 Group Theory :finite group G an element exactly two conjugate If in a finite group G an element a has exactly two conjugates, prove that G has a normal subgroup N ≠ e , G Please see the attached file for the complete solution.

  • Group Theory : Cycles and Permutation Groups

    89033 Group Theory : Cycles and Permutation Groups In Sn prove that there are (1/r). [n!/( n - r ) ] distinct r cycles. Please see the attached file for the complete solution.

View More Related Solutions