IIT JAM

follow

Top Resources

P

Prabhupada posted an Question

March 30, 2020 • 23:28 pm

30 points

IIT JAM
Mathematics (MA)

Show that if a group has order 2n ,for some n €n ,then the number of self inverse of that group is always even and greater than equal to 2.

show that if a group has order 2n ,for some n €N ,then the number of self inverse of that group is always even and greater than equal to 2.

1 Answer(s)

0 Likes
2 Comments
0 Shares

P
Prabhupada

here the identity 1 is self inverse of order 1 but not of order 2
- Likes(0)
- Reply(0)

S
Sumati priya

You should say that if a group is of even order then number of self - inverse elements of that group is always ODD . Check attached file.
- Likes(0)
- Reply(16)
but mam ..i said no of self inverse elements
- Like(0)
i am not asking that no of elements of order 2
- Like(0)
see.. suppose a group is {1,3,5,7} under multipication modulo 8
- Like(0)
here all these 4 are self inverse but the no of elements of order 2 is 3 ie 3,5,7
- Like(0)
your proof is also correct because you have shown that the number of element of order 2 is always odd...i agree
- Like(0)
Self inverse element means the element which is inverse of itself which follows that order of self inverse elements is 2. In a group { 1,3,5,7} under multiplication modulo 8 , self inverse elements are 3,5,7 and their number is 3 i.e, odd.
- Like(0)
but the identity 1 is also a self inverse
- Like(0)
because e is also inverse of itself
- Like(0)
yes yes identity is also self inverse. i forgot to say other than identity
- Like(0)
U are absolutely right..I forgot to consider indentity in the proof..I considered it as for no of elements of order 2.
- Like(0)
that's why i am saying that your proof is also correct
- Like(1)
btw thank you
- Like(0)
It's my pleasure. All the best 👍💯
- Like(0)
Mam...what happened to the number of self inverse element if the group is of odd order?
- Like(0)
please give me some counter examples
- Like(0)
only identity will be the self inverse element.
- Like(0)

T