Register

TIFR-2014-Maths-B-3

• edited by
566 views
1 votes
1 votes

Let $S_{n}$ be the symmetric group of $n$ letters. There exists an onto group homomorphism 

  1. From $S_{5}$ to $S_{4}$ 
  2. From $S_{4}$ to $S_{2}$ 
  3. From $S_{5}$ to $\mathbb{Z}/5$
  4. From $S_{4}$ to $\mathbb{Z}/4$
• edited by
User Avatar

Please log in or register to answer this question.

Voting & Accepting an answer helps improve the community
Answer:
← PreviousNext →
← Previous in categoryNext in category →

Related questions

1 votes
1 votes
0 answers
1
makhdoom ghaya asked Dec 17, 2015
366 views
TIFR-2014-Maths-B-5
Which of the following groups are isomorphic? $\mathbb{R}$ and $C$ $\mathbb{R}^{*}$ and $C^{*}$ $S_{3}\times \mathbb{Z}/4$ and $S_{4}$ $\mathbb{Z}/2\times \mathbb{Z}/2$ and $\mathbb{Z}/4$
Which of the following groups are isomorphic? $\mathbb{R}$ and $C$ $\mathbb{R}^{*}$ and $C^{*}$ $S_{3}\times \mathbb{Z}/4$ and $S_{4}$ $\mathbb{Z}/2\times \mathbb{Z}/2$ a...
User Avatar
1 votes
1 votes
0 answers
2
makhdoom ghaya asked Dec 9, 2015
367 views
TIFR-2011-Maths-B-3
There are n homomorphisms from the group $\mathbb{Z}/n\mathbb{Z}$ to the additive group of rationals $\mathbb{Q}$.
There are n homomorphisms from the group $\mathbb{Z}/n\mathbb{Z}$ to the additive group of rationals $\mathbb{Q}$.
User Avatar
2 votes
2 votes
0 answers
3
makhdoom ghaya asked Dec 9, 2015
515 views
TIFR-2011-Maths-B-7
There is a non-trivial group homomorphism from $S_{3}$ to $\mathbb{Z}/3\mathbb{Z}$.
There is a non-trivial group homomorphism from $S_{3}$ to $\mathbb{Z}/3\mathbb{Z}$.
User Avatar
2 votes
2 votes
4 answers
4
makhdoom ghaya asked Dec 17, 2015
2,707 views
TIFR-2014-Maths-B-4
Let $H_{1}$, $H_{2}$ be two distinct subgroups of a finite group $G$, each of order $2$. Let $H$ be the smallest subgroup containing $H_{1}$ and $H_{2}$. Then the order of $H$ is Always 2 Always 4 Always 8 None of the above
Let $H_{1}$, $H_{2}$ be two distinct subgroups of a finite group $G$, each of order $2$. Let $H$ be the smallest subgroup containing $H_{1}$ and $H_{2}$. Then the order o...
User Avatar
Link Copied!