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Nested symmetric representation of elements of the Suzuki chain groups. (English) Zbl 1040.20010

Symmetric presentations in the sense of R. T. Curtis are found for all the groups in the so-called Suzuki chain \[ L_3(2): 2< U_3(3): 2< J_2: 2< G_2(4): 2< 3\cdot \text{Suz}: 2 \] of subgroups of the Conway group \(\text{Co}_1\).

MSC:

20D08 Simple groups: sporadic groups
20F05 Generators, relations, and presentations of groups
20D06 Simple groups: alternating groups and groups of Lie type
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