Das, BireswarBireswarDasKumar, AnantAnantKumarSharma, ShivduttShivduttSharmaThakkar, DharaDharaThakkar2025-08-312025-08-312022-03-01[9783959772228]10.4230/LIPIcs.STACS.2022.252-s2.0-85127162527https://d8.irins.org/handle/IITG2025/26159A finite group of order n can be represented by its Cayley table. In the word-RAM model the Cayley table of a group of order n can be stored using O(n²) words and can be used to answer a multiplication query in constant time. It is interesting to ask if we can design a data structure to store a group of order n that uses o(n²) space but can still answer a multiplication query in constant time. We design a constant query-time data structure that can store any finite group using O(n) words where n is the order of the group. Farzan and Munro (ISSAC 2006) gave an information theoretic lower bound of Ω(n) on the number of words to store a group of order n. Since our data structure achieves this lower bound and answers queries in constant time, it is optimal in both space usage and query-time. A crucial step in the process is essentially to design linear space and constant query-time data structures for nonabelian simple groups. The data structures for nonableian simple groups are designed using a lemma that we prove using the Classification Theorem for Finite Simple Groups (CFSG).falseClassification Theorem for Finite Simple Groups | Compact Data Structures | Finite Groups | Simple Groups | Space Efficient RepresentationsConference Paper1 March 2022025cpConference Proceeding