Rakesh posted an Question
May 24, 2020 • 03:57 am 30 points
  • CSIR NET
  • Mathematical Sciences

Lfg= {1, (ac), (bd), (ab)(cd), (ac) (bd), (ad)bc), (abcd), (adbc)} {1, (ab)(cd), (ac) bd), (ad) (bc)} h and k= {1, (ab)(cd)} are sets of permutations, then (1)

lfG= {1, (ac), (bd), (ab)(cd), (ac) (bd), (ad)bc), (abcd), (adbc)} {1, (ab)(cd), (ac) bd), (ad) (bc)} H and K= {1, (ab)(cd)} are sets of permutations, then (1) H Ind and K both are normal subgroup of G. 2) K is normal subgroup of G but H is not a normal subgroup of G. (3) His normal subgroup ofG but K is not a normal subgroup of G. (4) H and K both are not normal subgroup of G.

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