L-2 Most Expected Questions - Abstract Algebra || CSIR-NET 2024

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[@debajitroy7300]

thank you Sir

[@keshavlalit1555]

First question me option c me If H has any atleast one reflection then order of class of reflection becomes 1011 that is not possible as we have order of H is 6 and also set of rotations in Dn is always subgroup and there is no subgroup of order 6 of Z(1011) as 6 does not divide 1011 so there does not exist any subgroup containing only rotations

[@Concept143]

Correct 👍

[@14-nasirhusain83]

Sir in first question.......option b
How to prove H is subgroup???

[@keshavlalit1555]

I think, if o(a) is odd let k and let o(b) is m then LCM(k,m ) also odd also order of b inverse is also m if we take power of ab^-1 as LCM then we get identity so order of ab^-1 must be odd