Understand the problem The multiplicative group (F^*_7) is isomorphic to a subgroup of the multiplicative group (F^*_{31}). Source of the problem TIFR GS 2018 Part A Problem 17 Topic Abstract Algebra Difficulty Level Medium Suggested Book Dummit and Foote Start with...

Understand the problem Let G be a finite group with a normal subgroup H such that G/H hasorder 7. Then (G cong) H × G/H. Source of the problem TIFR GS 2018 Part A Problem 23 Topic Group Theory Difficulty Level Medium Suggested Book Dummit and Foote Start with hints...

Understand the problem The permutation group (S_{10}) has an element of order 30. Source of the problem TIFR 2018 Part A Problem 23 Topic Group Theory Difficulty Level Easy Suggested Book Dummit and Foote Start with hints Hint 0Hint 1Hint 2Hint 3 Do you really need a...

Understand the problem Let A, B ∈ (M_n(Bbb R)) be such that A + B = AB. Then AB = BA. Source of the problem TIFR 2018 Part A Problem 19 Topic Linear Algebra Difficulty Level Medium Suggested Book Linear Algebra, Hoffman and Kunze Start with hints Hint 0Hint 1Hint...

Understand the problem True or False: Let A, B, C ∈ M3((mathbb{R})) be such that A commutes with B, B commutes with C and B is not a scalar matrix. Then A commutes with C. Source of the problem TATA INSTITUTE OF FUNDAMENTAL RESEARCH GS-2018 (Mathematics) Topic Linear...

Understand the problem The set of nilpotent matrices in (M_3(R)) spans (M_3(R)) considered as an R-vector space (a matrix A is said to be nilpotent if there exists n ∈ N such that (A^n = 0)). Source of the problem TIFR 2018 Part A, Problem 15 Topic LINEAR ALGEBRA...