On Connected Transversals to Subgroups Whose Order is a Product of Two Primes
نویسنده
چکیده
We consider finite groups which have connected transversals to subgroups whose order is a product of two primes p and q. We investigate those values of p and q for which the group is soluble. We can show that the solubility of the group follows if q = 2 and p ≤ 61, q = 3 and p ≤ 31, q = 5 and p ≤ 11. We then apply our results on loop theory and we show that if the inner mapping group of a finite loop has order pq where p and q are as above then the loop is soluble.
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عنوان ژورنال:
- Eur. J. Comb.
دوره 18 شماره
صفحات -
تاریخ انتشار 1997