Abstract
Let G be a finite group, and let Δ(G) be the prime graph built on the set of conjugacy class sizes of G: this is the simple undirected graph whose vertices are the prime numbers dividing some conjugacy class size of G, two vertices p and q being adjacent if and only if pq divides some conjugacy class size of G. In the present paper, we classify the finite groups G for which Δ(G) has a cut vertex.
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Acknowledgements
This research has been carried out during a visit of the third and fourth authors at the Dipartimento di Matematica e Informatica “Ulisse Dini” (DIMAI) of Università degli Studi di Firenze. They wish to thank the DIMAI for the hospitality.
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The research of the first and second authors is partially supported by the Italian PRIN 2015TW9LSR_006 “Group Theory and Applications” and by INdAM-GNSAGA.
The research of the third author is supported by the Spanish Ministerio de Ciencia e Innovación PID2019-103854GB-I00 partly with FEDER funds.
The fourth author acknowledges the support of the Spanish Ministerio de Ciencia, Innovación y Universidades proyecto PGC2018-096872-B-I00, the grant ACIF/2016/170 from Generalitat Valenciana, and the prize Borses Ferran Sunyer i Balaguer 2019.
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Dolfi, S., Pacifici, E., Sanus, L. et al. Groups whose prime graph on class sizes has a cut vertex. Isr. J. Math. 244, 775–805 (2021). https://doi.org/10.1007/s11856-021-2193-2
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DOI: https://doi.org/10.1007/s11856-021-2193-2