Computers in algebra: new answer, new questions (Q2747947)

The author introduces her own personal history of becoming known of and familiar with computers (operation and programming systems including user interface) for problems in algebra.NEWLINENEWLINENEWLINEHer previous reluctance changed to enthusiasm.NEWLINENEWLINENEWLINEThe power offered by the machines opened a wide field for solutions of deep and more specialised problems than hitherto seemed possible: especially when handling with permutation groups is involved. Also the Burnside problem with discontinuous groups is mentioned.NEWLINENEWLINENEWLINEAs much helpful for problem solution are named the systems SOGOS, CAS, CAYLEY, praised are MAGMA and especially GAP; and that for learning and teaching, too.NEWLINENEWLINENEWLINETogether with other computer aided solutions by using the system GRAPE is dicussed: the 1994 investigation of vertex-transitive non-Cayley graphs for a group relative to a self-inverse subset (goal: results on automorphisms): The case \(|G|=2pq\) with primes \(\text{mod }3 (4)\) led to several explicit families of permutation groups; using GRAPE she and her co-researchers finally could construct and examine the corresponding graphs. New results on matrix groups over finite fields will appear [in: Comput. Algebra, Foundations, Applications, Systems].NEWLINENEWLINENEWLINESuggestions are given of a few open questions on groups in algebra as candidates for use of computers.NEWLINENEWLINENEWLINEThe report ends with an outlook into the rest of this century, considering the fast growing capacity of computers and their systems for solution of questions in algebra, concerning speed, memory, and overcoming algorithms' complexity. Included are 59 references, mainly concerning permutation and other groups and use of computers for their analysis.