Abstract Mathematics help...?

1. let d7 =< a,b|a7 = e,b2 = e,bab = a-1 > dihedral group of order 14. prove no element of < > has order 2. prove every element of d7 not in < > has order 2.
2. let dn =< a,b|an = e,b2 = e,bab = a-1 > dihedral group of order 2n. prove each element of b not in < > has order 2.
3. let n , let dn =< a,b|an = e,b2 = e,bab = a-1 > dihedral group of order 2n. prove an∕2 commutes each element of dn. prove an∕2 nonidentity element of dn commutes each element of dn.
4. let h < g , let a,b g. prove ah = bh if , if b-1a h.
5. let h < g , let a,b g. can proof above modified prove ah = bh if , if ab-1 h?
6. let g group of order p2. prove g has element of order p.
7. let g group , let h , k subgroups of g, prove h ⋂ k subgroup of g.
8. let g group of order n , assume m integer relatively prime n. if gm = e prove g = e.
9. let g =< g > cyclic group of order 18. how many elements of g have order 18? how many elements h g satisfy h18 = e.
10. let g group of order 25. assume g not cyclic. prove each element of g satisfies g5 = e.

1. let d7 =< a,b|a7 = e,b2 = e,bab = a-1 > dihedral group of order 14. prove no element of < > has order 2. prove every element of d7 not in < > has order 2. 2. let dn =< a,b|an = e,b2 = e,bab = a-1 > dihedral group of order 2n. prove each element of b is...

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