3. Let G be a finite group of order |G| = n. Prove that G is isomorphic to a subgroup of Sym(G) since |G| = n, we have Sym(G) = Sn. Sn. Recall that for any set X, Sym(X) denotes the group of permutations of X;

3. Let G be a finite group of order |G| = n. Prove that G is isomorphic to a subgroup of Sym(G) since |G| = n, we have Sym(G) = Sn. Sn. Recall that for any set X, Sym(X) denotes the group of permutations of X;

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.4: Cosets Of A Subgroup

Problem 11E: Let be a group of order 24. If is a subgroup of , what are all the possible orders of ?

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3. Let G be a finite group of order |G| = n. Prove that G is isomorphic to a subgroup of
Sym(G)
since |G| = n, we have Sym(G) = Sn.
Sn. Recall that for any set X, Sym(X) denotes the group of permutations of X;

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