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Topic: Frobenius'group
Replies: 12   Last Post: Nov 8, 2010 6:20 AM

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Derek Holt

Posts: 498
Registered: 12/13/04
Re: Frobenius'group
Posted: Oct 16, 2010 4:46 AM
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On 16 Oct, 07:15, AP <marc.picher...@wanadoo.fr.invalid> wrote:
> is it true that two Frobenius'groups with same order are isomorphic?
> (I read very often : "the" Frobenius'group of order 20)
> Thanks


No, for example there are two non-isomorphic Frobenius groups of order
72, one with cyclic and one with quaternion complement.

G1 = < (2, 4, 5, 8, 3, 7, 9, 6),
(1, 2, 3)(4, 5, 6)(7, 8, 9) >

G2 = < (2, 4, 3, 7)(5, 6, 9, 8),
(2, 9, 3, 5)(4, 6, 7, 8),
(1, 2, 3)(4, 5, 6)(7, 8, 9) >.

Frobenius groups of prime degree are uniquely determined by their
order, but not in general.

Derek Holt.



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