[FOM] Query on alternating groups
joeshipman at aol.com
Tue Jan 3 16:06:24 EST 2006
I am looking for results on the orders (or, equivalently, the indexes)
of maximal subgroups of the alternating groups An.
An example of the kind of result I am looking for would be something
"for sufficiently large n, the maximal subgroups of An have indexes n,
n(n-1)/2, n(n-1)(n-2)/6, .... down to the middle binomial coefficient,
dividing the last term by an extra factor of 2 when n is even"
Examination of cases suggests that a set of "degree axioms"
D(i1),D(i2),...,D(i_j) entails the degree axiom D(n) when it includes
all the primes dividing n as well as any number expressible as a sum of
indexes of maximal subgroups of An.
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