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Frobenius groups generated by two elements of order 3. (Russian, English) Zbl 1003.20029
Sib. Mat. Zh. 42, No. 3, 533-537 (2001); translation in Sib. Math. J. 42, No. 3, 450-454 (2001).
A group \(G\) is called a Frobenius group if there are a proper nontrivial normal subgroup \(F\) and a subgroup \(H\) such that (a) \(G=FH\), \(F\cap H=1\), (b) \(H\cap H^g=1\) for every \(g\in G\setminus H\), (c) \(F\setminus\{1\}=\bigcap_{g\in G\setminus H}(G\setminus H^g)\).
The author gives a complete list of Frobenius groups generated by two elements of order three.

MSC:
20E34 General structure theorems for groups
20F05 Generators, relations, and presentations of groups
20D40 Products of subgroups of abstract finite groups
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