Abstract
In this note, we derive a criterion for determining when two groups generate the same group variety. We use this, along with a description of the 2-variable word maps on the dihedral, dicyclic, and semi-dihedral groups, to show that the maximal class 2-groups of the same order generate the same variety.
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Acknowledgements
This material is based upon work done while the first author was supported by the National Science Foundation under Grant no. DMS-1502553. The first author’s efforts were partially funded by a GEN Omar N. Bradley Officer Research Fellowship in Mathematics.
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Presented by: Peter Mayr.
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Cocke, W., Skabelund, D. The maximal class 2-groups generate the same variety. Algebra Univers. 82, 17 (2021). https://doi.org/10.1007/s00012-020-00704-3
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DOI: https://doi.org/10.1007/s00012-020-00704-3