#17 please föř áll å, 6 in8. Prove that a group G is Abelian if and only ifG"9. In a group, prove that (@"')" - a10. If “.4..4, is an element in a group, what is (a,a:-a,) = ?11. Prove that every Cayley table is a Latin square for a group. That is,each element of the group appears exactly once in each row and eachcolumn of a Cayley table.12. Suppose the table below is a group table. Fill in the blank entries:elea b l|b cde13. Prove that if (ab)' = a*b* in a group G, then ab = ba.14. Prove that the set of all rational number of the form 3"6" | m,nEZ} is agroup under multiplication.15. Let G be a group and let g be in G. Define a function *- :G -→ G by$,(x) = gxgShow that .:G→G is one-to-oneand onto.16. Let G be a group and let g and h be in G. Show that . E.defined in #15.17. Prove that if G is a group with the property that the square of everyelement is the identity, then G is Abelian.as

Name: #17 please föř áll å, 6 in8. Prove that a group G is Abelian if and on
Uploaded: 2024-03-05T11:52:21.000Z
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Description: #17 please föř áll å, 6 in8. Prove that a group G is Abelian if and only ifG"9. In a group, prove that (@"')" - a10. If “.4..4, is an element in a group, what is (a,a:-a,) = ?11. Prove that every Cayley table is a Latin square for a group. That is,ea