Abstract Classes ®

best optional for UPSC 2024

Free UPSC Mathematics Optional Paper-2 2024 Solutions: View Online | UPSC Maths Solution | IAS Maths Solution

SECTION-A Question:-1(a) Let G G GGG be a finite group of order m n m n mnmnmn, where m m mmm and n n nnn are prime numbers with m > n m > n m > nm > nm>n. Show that G G GGG has at most one subgroup of order m m mmm.

best optional for UPSC 2024

Free UPSC Mathematics Optional Paper-1 2024 Solutions: View Online | UPSC Maths Solution | IAS Maths Solution

Question:-1(a) Let H H HHH be a subspace of R 4 R 4 R^(4)mathbb{R}^{4}R4 spanned by the vectors v 1 = ( 1 , − 2 , 5 , − 3 ) v 1 = ( 1 , − 2 , 5 , − 3 ) v_(1)=(1,-2,5,-3)v_{1}=(1,-2,5,-3)v1=(1,−2,5,−3), v 2 = ( 2 , 3 ,