Abstract
In this paper, we show that for the alternating group An, the class C of n- cycle, CC covers An for n when n = 4k + 1 > 5 and odd. This class splits into two classes of An denoted by C and C/, CC= C/C/ was found.
Highlights
For every class in A9, a conjugate b of a can be found such that ab represents that class
This assertion is the substance of the table below b ab a – 1
If P contains no cycle longer than transposition, either P is of type 22k 11, whence CC contains P by the lemma, or we have
Summary
Bertram showed that if n is odd is the n – cycles in An fall into two conjugate classes C, C/, and for the (n – 1) – cycles if n is even, so that the quoted results does not decide whether For every class in A9, a conjugate b of a can be found such that ab represents (line in) that class. N 1 (mod 8) n – 1 = 8k n = 8k +1 n = 8k +1, n > 9 If k = 1 n = 9 x = (967852341) is conjugate to a and ax = (13)(24)(57)(68)
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