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Math Help - Frobenius Groups

  1. #1
    Junior Member
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    Frobenius Groups

    I have searched through 2 books by Ledermann on group theory and cannot find any proofs to these questions.
    Can anybody help?

    1.Prove that a finite Group G with a nilpotent subgroup of prime-power
    index pn say, is soluble.
    2. Show that the centre of a Frobenius group is always trivial.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by Turloughmack View Post
    I have searched through 2 books by Ledermann on group theory and cannot find any proofs to these questions.
    Can anybody help?

    1.Prove that a finite Group G with a nilpotent subgroup of prime-power
    index pn say, is soluble.
    2. Show that the centre of a Frobenius group is always trivial.
    For 1. do you have normality? If so, |G/H|=p^n so G/H is nilpotent, and so is H, so...

    For 2. I'll give you a hint: how does the centre act on H by conjugation, where H is the subgroup such that H^x\cap H = 1?
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