Let a be a group element and lal = o0. Complete the following statement: la'l = la'l if and only if ....

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Let a be a group element and lal = o0. Complete the following
statement: la'l = la'l if and only if ....
Transcribed Image Text:Let a be a group element and lal = o0. Complete the following statement: la'l = la'l if and only if ....
Expert Solution
Step 1

Given that a be a group element and a=.

We need to complete the statement: ai=aj if and only if ......

Step 2

If part:

ai=aj

Let ai=aj=k

We get,

ai·ai·.....·aik-times=aj·aj·....·ajk-times=eidentityaik=ajkaik=ajkaik·a-jk=ajk·a-jk                ajkG a-jkGaik-jk=a0aik-jk=e

Since a=, we get ik-jk=0

ik-jk=0ik=jki=j

If ai=aj and a=, then i=j.

Conversely:

If i=j

ai=aj implies ai=aj

If i=j then ai=aj.

Therefore, a= and ai=aj if and only if i=j.

steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,