2022/07/30 by Khyati Sharma, Sharma, Khyati, A. Satyanarayana Reddy +1 · 1 citation
Computer Science · Mathematics · #20D10 #20D99 #Computability, Logic, AI Algorithms #FOS: Mathematics #Group Theory (math.GR) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2208.01415
openalex publication_date 2022/07/30 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
A finite group is called a CLT-group if it contains a subgroup corresponding to every divisor of the order of the group. It is said to be a Cyclic (Abelian) CLT group if it contains a cyclic (abelian) subgroup corresponding to every proper divisor of the order of the group. A natural number is said to be a CCLT (ACLT) number if every group of that order is a cyclic (abelian) CLT group. In this work, we classify all CCLT and ACLT numbers and study various properties of Cyclic (Abelian) CLT groups. We also show that the classes of CCLT and ACLT groups are contained in the class of supersolvable groups. Moreover, we introduce the function CCLT-degree on the set of non-cyclic finite groups and study the properties of this function.