Question

Subject: Abstract Algebra

Please help me out with these problems through proofing. There are two parts to it.

Suppose G is a group, with a belong to G.

a. Prove that a^ma^n = a^m+n for all natural numbers m and n. Hint: Fix n belong to N. Then prove by mathematical induction on m.

b. Prove that (a^m)^n = a^mn for all natural numbers m and n.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Advanced Math

Related Advanced Math Q&A

Find answers to questions asked by students like you.

Q: Differential equations: Using the power series method, find the particular solution to the initial v...

A: Consider the given initial value problem:

Q: Use a truth table to determine whether this argument is valid or invalid: VALID INVALID p V q TITIT ...

A: To analyze the correctness of the logic .

Q: Pls explain to me step by step. Pls dont skip ay steps. thanks

A: Suppose P=(x0,y0) is an critical point of the system x\'=f(x,y) , y\'=g(x,y),and that f and g are di...

Q: Advanced Math Question

A: To construct a Truth Table for the given statement ,  first find the conjunction of p  and  q  then ...

Q: Abstract Algebra (Proof writing): Looking for assistance on this problem.

A: Consider the function φ:Z/6Z ->Z6  ,

Q: Subject: Elements if Set Theory By Herbert B. Enderton   Having trouble with a written assignment gi...

A: It is required to prove the given set theoretic identities using mathematical induction

Q: 6. A croissant shop has 7 types of croissants: plain, cherry, chocolate, almond, apple, cheese and h...

A: (a) The shop has 7 types of croissants.So n = 7. To choose one dozen croissants, so r = 12.Repetitio...

Q: Show that if charL(x) has a non-zero root, then for all m>0 we have Lm≠0. Explain what this means...

A: To relate non-zero eigenvalues and the characteristic polynomial of a linear operator

Q: 5. Let (n) be a uniformly bounded sequence of functions which are Riemann integrable on [a, b, and p...

A: By the hypothesis there exists an real number M such that Supremum of x belongs to [a,b] of |fn(x)|&...

Q: 16. Does this graph have an Eulerian circuit? If not, why not? If so, list one. List a Hamiltonian c...

A: To investigate the given graph for the required circuit  properties

Q: the book is "First Course on Fuzzy Theory and Applications"

A: We are going to find the Distances by the following methods:

Q: Subject: Elements if Set Theory By Herbert B. Enderton   Having trouble with a written assignment gi...

A: To establish the formula for the sum of the first n squares, using induction.

Q: (5) Let p(t) denote the population of the Earth in the year t. According tothe internet, p(2017) = 7...

A: The differential equation for population growth is given.

Q: Define f: R->R as follows: f(x)=x-[x] if [x] is even. f(x)=x-[x+1] if [x] is odd. Determine those...

A: To find the points where the given function is continuous.Take two cases:Case 1: Let x = a is an eve...

Q: Proposition: Let e be an edge of a triangulation, where e = AC belongs to the two triangles ABC and ...

A: To prove that D is located outside the circumcircel of the triangle ABC, under the given conditions

Q: the book is "First Course on Fuzzy Theory and Applications"

A: Consider the given fuzzy relation:

Q: See attachment.  I am able to show that it is an equivlance relation, and so I don't need help with ...

A: First we need to show that the given relation is an equivalence relation.For a relation to be an equ...

Q: How many ways can you choose 5 out of 10 friends to invite to a dinner party?

A: To solve the problem of combinations (selections) in the given scenario.

Q: Differential equations Consider the vectors x1(t) and x2(t) Please refer to attached image for vecto...

A: Obtain the Wronskian of the vectors as follows.

Q: Find a graph or bar chart that represents a real situation where you could use a linear or exponenti...

A: Consider a real life situation:Suppose that you are taking a cab. You know that the cab service char...

Q: An experiment consists of tossing a coin seven times and observing the sequence of heads and tails1)...

A: Given:An experiment consists of tossing a coin seven times and the outcomes are the sequence of head...

Q: DIFFERENTIAL EQUATIONS Refer to the given 3x3 coefficient matrix with initial conditions (see attach...

A: To solve we have to find eigen vectors for this we have to find eigen values.To find eigen values,Ta...

Q: Chapter 1 Section 1.2 19. A section of a gear is shown. Given the formulas below and the circular pi...

A: Formula used: 

Q: Find the critical points and sketch the phase portrait of the given autonomous first order different...

A: Consider the provided autonomous first order differential equation.

Q: 8. Suppose a vending machine accepts $1 bills, $1 silver coins and $1 gold coins, $3 bills and $3 go...

A: 8.a. To find the recurrence relation for the number of ways to deposit n dollars in the vending mach...

Q: r2 -2e = 0 has a solution in the interval -1,1] 6. (10 points) The equation f(x) (a) (5 points) With...

A: (a) The given equation is f(x) = x2 – 2ex = 0 has a solution in the interval [−1, 1].       The seca...

Q: Please answer number 2. Thanks

A: To  trace the sources (authors) and interpret the expressions in modern notation

Q: Z is a complex variable z=x+iy  question attached as photo

A: To determine all the functions satisfying the given condtions

Q: Question1-: (Filter generated by a family of sets). Let S ⊆ ℘(X) be nonempty family of subsets of X,...

A: As per norms, question 1 ( 3 subparts ) are answered. The problem concerns filters generated by fami...

Q: DIFFERENTIAL EQUATIONS: Using the power series method, solve the given initial value problem: y"+x2y...

A: Click to see the answer

Q: Solve the differential equation using either the method of undetermined coefficients or Laplace tran...

A: The differential equation is y′″ -6y″+11y′-6y = 3x.

Q: the book is "First Course on Fuzzy Theory and Applications"

A: To  write down the table for the fuzzy composite relation

Q: Differential equations. Find the particular solution to given system of equations. please refer to a...

A: To solve the IVP, first obtain the eigenvalues and eigenvectors for the matrix as follows.

Q: the book is "First Course on Fuzzy Theory and Applications"

A: Consider Part a) and use the following:

Q: 6.11  the book is "First Course on Fuzzy Theory and Applications"

A: Given fuzzy function 

Q: Subject: College Geometry (Proofs)Book: Euclidean and Non-Euclidean GeometriesI could really need so...

A: Click to see the answer

Q: Pls explain to me step by step and pls dont skip any step. Thanks

A: To prove that the taxicab distance is actually a metric on the plane

Q: please solve the question no 3-7

A: Hello. Since your question has multiple parts, we will solve first three parts (3-5 in this case) fo...

Q: Z is a complex variable, z=x+iy

A: The z is complex variable with z = x + i y , and the given vertices are (0,0),(1,0),(1,1) and (0,1).

Q: Find the solution to the given initial value problem. 4y"-12y'+9y=0, y(0)=0, y'(0)=1

A: The given initial value problem is y"-12y’+9y=0 with initial condition y(0)=0 and y’(0)=1.

Q: At age 22​, someone sets up an IRA​ (individual retirement​ account) with an APR of 8​%. At the end ...

A: Formula used:Future value of an ordinary Annuity: