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
• DOI: 10.1006/eujc.1997.0163

✦ 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.