• Want FREE Counselling for Exam Preparation?
###### Call Us
800-355-2211

Speak With a Friendly Mentor.

###### Vijay posted an Question
September 30, 2021 • 08:20 am 30 points
• IIT JAM
• Mathematics (MA)

# Iexample 1 the set of

please send the solution to the problem given in the attachment.

• 0 Likes
• 0 Shares
• ##### Deepak singh 1

Refer attachment

then why do we claim 1 is a generator of Z as 1 only generates half of the Z set and by the definition of a generator 1 was supposed to be generating the whole Z set, isn't it?

Generators of Z are 1 and -1 . ( not only 1)

what is the definition of a generator?

check

each elements of group can written as some integral power of a then a is generator of G

abhi bhi -ve integers generate nahi ho rahe

Negative no. will be generated by ' -1 ' and +ve will be generated by ' 1' . Therefore generators of Z are {-1,1} .

but that is not the definition of a generator

how ?

the generator is supposed to generate all the elements of a group.

its not necessary that generator is unique . In case of Z there are two generators.

doubt

??

your +ve one is correct and -ve one will be in this way

Read Dummit . It will clarify your doubt .

this book is not available in my library kindly send me the bookish definition of the generator if possible for you because now I am confused with the generator definition.

a generating set of a group is a subset of the group set such that every element of the group can be expressed as a combination (under the group operation) of finitely many elements of the subset and their inverses.

### Do You Want Better RANK in Your Exam?

Start Your Preparations with Eduncle’s FREE Study Material

• Updated Syllabus, Paper Pattern & Full Exam Details
• Sample Theory of Most Important Topic
• Model Test Paper with Detailed Solutions
• Last 5 Years Question Papers & Answers