Question: G is a group acting on a set X. S is a set. Let M(X, S) to be the set of all functions X ??

G is a group acting on a set X. S is a set. Let M(X, S) to be the set of all functions X ?? S. (i). Prove (g.f)(x) = f(g ?1 .x) defines a group action of G on M(X, S). (ii). If S has more than one elements, prove the action defined above is not transitive.

G is a group acting on a set X. S is a set. Let M(X, S) to be the set of all functions X - S. (i). Prove (g.f)(x) = f(g .x) defines a group action of G on M(X, S). (ii). If S has more than one elements, prove the action defined above is not transitive

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

1 Assumptions and Calculated Values 2 Bank Rate Information: Flynn's Bank Account Rate (compounded monthly) Monthly Bank Rate Effective Annual Interest Rate Salary and Bonus Information: Annual...

Let G be a group acting on a set X . Then there is an induced ( diagonal ) action of G over X \ times X defined by g ( x , y ) = ( gx , gy ) . We say that the action of G on X is doubly transitive if...

MTH 411-1 Abstract Algebra II S17 Homework 7 due on 3/22/17 1. Let G be a group acting on the set I. Let i I and g G. Show that StabG (gi) = gStabG (i)g 1 . For the remaining exercises let F be a...

Bonus (10 points): Let G be an abelian group acting on a set X. Suppose that there is only one orbit under this action. Assume that |G| |X|. Prove that there exists ege G such that Fix(g) = X.

Let G be a group acting on a set S containing at least two elements. Assume that G is transitive; that is, given any x,y S, there exists g G such that gx = y. Prove (a) for x S, the orbit x of x...

Bonus (10 points): Let G' be an abelian group acting on a set X. Suppose that there is only one orbit under this action. Assume that |G| 75 |X|. Prove2 that there exists 6 75 g E G' such that Fix(g)...

Let (G, ) be a group and X any set. Define F to be the set of functions f : X G and define a binary operation ? on F as follows: f ?g : X G is the function given by (f ?g)(x) := f(x)g(x) x X. Is (F,...

Problem 1. Let X be a nonempty set. A partition of X is a finite collection of non-empty disjoint subsets of X, P = {X, X, ..., X}, such that X = X UX U... U Xk. We say that the positive integer k is...

Problem 9 Suppose G acts on the left on the set X via p : G x X - X. Let p : G - Sx be the corresponding permutation representation. Define the set of fixed points X of G in X as X" = {xEX| g . x = x...

3 ,,uoh "gram 3 Eww 3 m T mm H a 3 .2 ' m w .,.m.av>v 3. m. @3on we geonwoaoa mm H "with M'nr H E. wads + we A at. ES 0 3.8V WEE 3563 mo wow 23 E m \"9H .3 avgmeMm\" mnemagouom Aggy\"...

Why is the common stockholder referred to as a residual claimant?

What steps are followed in posting from the purchases journal to the general ledger?

If a county collects taxes on behalf of the city and school district, it would record the taxes in the Question 7 0 options: Special Revenue Fund. Agency Fund. Trust Fund. General Fund.

2023 1040 form 1.Phillip and Claire are married and file a joint return. Phillip is self-employed as a real estate agent, and Claire is a flight attendant. Phillip and Claire have three dependent...