Abstract
We introduce some special system of generators on finite groups, that we call diagonal double Kodaira structures and whose existence is equivalent to the existence of some special Kodaira fibred surfaces, that we call diagonal double Kodaira fibrations. This allows us to rephrase in purely algebraic terms some results about finite Heisenberg groups, previously obtained in Causin and Polizzi (Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XXII:1309–1352, 2021), and makes possible to extend them to the case of arbitrary extra-special p-groups.
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Acknowledgements
The author was partially supported by GNSAGA-INdAM. He thanks Andrea Causin for useful comments and remarks. He is also grateful to the organizers of the 12th ISAAC Congress, Universidade de Aveiro (2019), and in particular to Alexander Schmitt, for the invitation and the hospitality. Finally, he is indebted with Geoff Robinson and Derek Holt for their generous help with the proof of Lemma 3.9, see the MathOverflow thread https://mathoverflow.net/questions/351163, and to the anonymous referee for constructive criticism and precise suggestions that considerably improved the presentation of these results.
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Polizzi, F. (2022). Diagonal Double Kodaira Structures on Finite Groups. In: Cerejeiras, P., Reissig, M., Sabadini, I., Toft, J. (eds) Current Trends in Analysis, its Applications and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-87502-2_12
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DOI: https://doi.org/10.1007/978-3-030-87502-2_12
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