3 research outputs found
On exceptional groups of order p^5
A finite group G is exceptional if it has a quotient Q whose minimal faithful
permutation degree is greater than that of G. We say that Q is a distinguished
quotient.
The smallest examples of exceptional p-groups have order p^5. For an odd
prime p, we classify all pairs (G,Q) where G has order p^5 and Q is a
distinguished quotient. (The case p=2 has already been treated by Easdown and
Praeger.) We establish the striking asymptotic result that as p increases, the
proportion of groups of order p^5 with at least one exceptional quotient tends
to 1/2.Comment: 23 page
On exceptional groups of order p⁵
A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient.
The smallest examples of exceptional p-groups have order p5. For an odd prime p, we classify all pairs (G, Q)where G has order p5 and Q is a distinguished quotient. (The case p = 2 has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order p5 with at least one exceptional quotient tends to 1/2