Mathematics · Group Theory
Let G be the cyclic group of order 8 and H = S5 be the symmetric permutation group of 5 elements. Which of the following statements is necessarily true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
Share:
- 1There are fewer than 10 different group homomorphisms from G to H.
- 2There exists a surjective group homomorphism from G to H.
- 3There exists no injective group homomorphism from G to H.✓
- 4There exists no nontrivial group homomorphism from G to H.
Correct answer
There exists no injective group homomorphism from G to H.
Download Single Question PDF
Save this question and verified answer as a clean study sheet with live clickable link.
👥
Share with Friends & Study Groups
Challenge your peer aspirants on WhatsApp or Telegram to solve this question!
Online Test Series
Preparing for Mathematics?
Practice full-length Mathematics mock tests with real exam timers, instant score analysis, and all-India ranking.
Chapter Practice
Practice Group Theory MCQs →Want more practice questions on Group Theory?
Solve complete topic-wise tests with detailed solutions on GkGet.
Related Practice Questions
Recommended practice questions in Mathematics · Group Theory