DSTL Unit 4 Notes AKTU (BCS303)

AKTU · BTECH · Semester 3 · Discrete Structures & Theory of Logic · Unit 4 · Notes

AKTU Discrete Structures & Theory of Logic (BCS303) Unit 4 notes for B.Tech Semester 3 – Algebraic Structures (Group Theory). Topics: Groups & Subgroups…

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Unit 4: Algebraic Structures (Group Theory) – AKTU syllabus topics

  • Groups & Subgroups: Cyclic Groups, Permutation & Symmetric Groups
  • Cosets & Lagrange's Theorem
  • Group Homomorphism
  • Rings & Fields

Most asked AKTU PYQ questions from Unit 4

  1. Q3a. Let G = {1,-1, i, -i} with the operation of ordinary multiplication on G be an algebraic structure, where i=√-1. (i) Determine whether G is abelian. (ii) Determine the order of each element in G. (iii) Determine whether G is a cyclic group, if G is a cyclic group, then determine the… (10 marks, 2022-23)
  2. Qb. How many generators are there of the cyclic group G of order 10. (7 marks, 2025-26)
  3. Q6a. Calculate the number of generators of the cyclic group of order 8. (7 marks, 2024-25)
  4. Q2d. Let G= {1, -1, i, - i} with the binary operation multiplication be an algebraic structure, where i = √-1 then determine whether G is an Abelian group. Also if G is cyclic Group, then determine the generator of G. (7 marks, 2023-24)
  5. Q1c. State and justify “Every cyclic group is an abelian group”. (2 marks, 2021-22)
  6. Q1d. State Ring and Field with example. (2 marks, 2021-22)
  7. Q1d. Define ring. (2 marks, 2020-21)
  8. Q1d. Show that every cyclic group is abelian. (2 marks, 2019-20)
  9. Q3b. Let (G,*) and G’,*’) be any two groups and let e and e’ be their respective identities. If f is a homomorphism of G into G’, then prove that (i) f(e) = e’ (ii) f(x-1) = [f(x)]-1 , ∀ x ∈G (10 marks, 2022-23)
  10. Q7a. Prove that the set of residues F={0,1,2,3,4} modulo 5 is a field w.r.t. addition and multiplication of residue classes modulo 5. i.e. (F, +5, X5) is a field. (10 marks, 2022-23)

AKTU paper codes: BCS303, KCS303, BCS303H, KCS303H

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