Answer to Question #47362 in Abstract Algebra for ayush kumar

Question

1. a) Let G be a group of order 36 with 4 Sylow- 3 subgroups. Show that the intersection of any two of
these subgroups is of order 3.

(b) Prove by induction that 2n > 2n + 3 v n > 4.

(c) Express the following permutation as the product of disjoint cycles:
( 1 2 3 4 5 ) ( 2 4 7 )
( 3 1 5 2 4) (4 7 2 )