The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
0 votes
36 views

Let $G$ be a finite group of even order. Then which of the following statements is correct?

  1. The number of elements of order $2$ in $G$ is even
  2. The number of elements of order $2$ in $G$ is odd
  3. $G$ has no subgroup of order $2$
  4.  None of the above.
in Set Theory & Algebra by Boss (41.1k points) | 36 views

1 Answer

0 votes
Answer is B.

Since the group is of even order and the identity is the inverse of itself, therefore, there are odd number of elements (other than identity).

Also, if there is some element which is not inverse of itself, then we can pair such elements with their inverses. This will leave us with odd number of elements which have to be their own inverses.
by Active (1.2k points)

Related questions

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
49,807 questions
54,727 answers
189,302 comments
79,846 users