The Existence of Triple Factorizations for Sporadic Groups of Rank 3
https://doi.org/10.18255/1818-1015-2015-2-219-237
Abstract
A finite group G with proper subgroups A and B has triple factorization G = ABA if every element g of G can be represented as g = aba0 , where a and a 0 are from A and b is from B. Such a triple factorization may be sometimes degenerate to AB-factorization. The task of finding triple factorizations for a group is fundamental and can be used for understanding the group structure. For instance, every simple finite group of Lie type has a natural factorization of such a type. Besides, the triple factorization is widely used in the study of graphs, geometries and varieties. The goal of this article is to find triple factorizations for sporadic groups of rank 3. We have proved the existence theorem of ABA-factorization for sporadic simple groups McL and F i22. There exist two rank 3 permutation representations of F i22. We have proved that ABA-factorizations exist in both cases.
About the Authors
L. S. Kazarin
P.G. Demidov Yaroslavl State University
Russian Federation
Sovetskaya str., 14, Yaroslavl, 150000, Russia
Russian Federation
Sovetskaya str., 14, Yaroslavl, 150000, Russia
I. A. Rassadin
ООО «Нетис Телеком»
Russian Federation
исследователь
Russian Federation
исследователь
D. N. Sakharov
ООО «Агентство развития «4Р»
Russian Federation
исследователь
Russian Federation
исследователь
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Review
For citations:
Kazarin L.S., Rassadin I.A., Sakharov D.N. The Existence of Triple Factorizations for Sporadic Groups of Rank 3. Modeling and Analysis of Information Systems. 2015;22(2):219-237. (In Russ.) https://doi.org/10.18255/1818-1015-2015-2-219-237
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