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4. (a) Define when two elements of a group are conjugate to each other. State and de- duce the cl...

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4. (a) Define when two elements of a group are conjugate to each other. State and de- duce the class equation using the decom

4. (a) Define when two elements of a group are conjugate to each other. State and de- duce the class equation using the decomposition of a group in conjugacy classes (b) Let G be a finite group and p a prime number such that p divides G. Prove that there is a subgroup H of G such that |H p. (c) Let p be a prime number. Prove that any positive integer n, any group with p" elements is solvable
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its the claりoftlese equation should be decomposwon and tioue Cl P di vide IGl and hl aeNo taen hon ela ℉up with ↑n to, .la elem..tr !s Solvbu-2 ndut chon ョ ャ abelian gar an d tS

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