exercise 3 let g be a group of order 52 72 19 23275 a prove that g con
Exercise 3 Let G be a group of order 52-72-19-23275.
(a) Prove that G contains exactly one subgroup of order 49. Prove furthermore that if N <G with |N|
then N is normal.
(b) Prove that G/N is isomorphic to either Z19 × Z25 or Z19 × Z5 X Z
Suggestion: Similar to the Exercise 2c, exept apply Proposition 3.7.1 instead of 3.7.7.
(c) Let Ps and P19 be Sylow 5- and 19-subgroups of G, respectively. Prove that NP5 and NP19 are both subgroups
of G and that
NPN X P5, and NP19 N x P19-
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