A contribution to the analysis of a reduction algorithm for groups with an extraspecial normal subgroup

作者：Cagman Abdullah; Ankaralioglu Nurullah^*

来源：Turkish Journal of Mathematics, 2016, 40(4): 914-923.

DOI：10.3906/mat-1506-35

• Extraspecial group
• matrix group
• reduction algorithm
• algorithm analysis

Reduction algorithms are an important tool for understanding structural properties of groups. They play an important role in algorithms designed to investigate matrix groups over a finite field. One such algorithm was designed by Brooksbank et al. for members of the class in Aschbacher's theorem, namely groups N that are normalizers in GL(d, q) of certain absolutely irreducible symplectic-type r-groups R, where r is a prime and d = r(n) with n > 2. However, the analysis of this algorithm has only been completed when d = r(2) and when d = r(n) and n > 2, in the latter case under the condition that G/RZ(G) congruent to N/RZ(N). We prove that the algorithm runs successfully for some groups in the case of d= r(3) without any assumption.

• 出版日期2016