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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Mathematics (MA)
Iexample 1 the set of
please send the solution to the problem given in the attachment.
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Deepak singh 1![best-answer]()
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.