search
Log In
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
1 vote
111 views

in Set Theory & Algebra 111 views

1 Answer

5 votes
 
Best answer

Here we are given that the order of the group is 10 and a is the generator..

Hence  a10  =  e  where e is the identity element but we dont know about a8..Hence we have to write it in terms of a10 as that is a known result.

Let we have   y  =  a40   which can be written as :    a40  =   (a10)4   =  e4   =   e    ...(1) 

                                                            Also ,        a40   =  (a8)5     =  e     [ Follows from (1) ]

Hence it means that  a8 is repeated 5 times in order to get the identity element e which is least number of times to do so.

Also from the corollary of the Lagranges' Theorem , 

Order of an element  divides the order of the order of the group (The actual theorem is order of a subgroup divides the order of the group)

Here 5 divides the order of group i,e, 10..

Hence order of  a8   =   5 


selected by

Related questions

1 vote
1 answer
1
121 views
Plz explain this question
asked Oct 2, 2017 in Set Theory & Algebra Rishi yadav 121 views
3 votes
0 answers
2
154 views
Let < G, * > be a finite group and let H1 and H2 be it's sub group as per lagrange theorem we know order of sub group divides order of group, my doubt is, is it possible that we can have multiple subgroup of same cardinality for a particular group ? $\left | H1 \right |=\left | H2 \right |$
asked Oct 21, 2017 in Set Theory & Algebra Tesla! 154 views
0 votes
0 answers
3
117 views
#plz check i think 2nd property hold in reverse way??
asked Jan 27, 2017 in Set Theory & Algebra Hradesh patel 117 views
0 votes
1 answer
4
112 views
I Have doubt about the language. Is it asking about the sum of elements if we make the GBL set for the given lattice .
asked May 20, 2019 in Set Theory & Algebra Shawn Frost 112 views
...