𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On Connected Transversals to Subgroups Whose Order is a Product of Two Primes

✍ Scribed by Markku Niemenmaa


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
70 KB
Volume
18
Category
Article
ISSN
0195-6698

No coin nor oath required. For personal study only.

✦ Synopsis


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.