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The main goal in this paper is to use a dual equivalence in automata theory started in [RBBCL13] and developed in [BBCLR14] to prove a general version of the Eilenberg-type theorem presented in [BBPSE12]. Our principal results confirm the existence of a bijective correspondence between formations of (non-necessarily finite) monoids, that is, classes of… (More)
For a finite group G we define the graph Γ(G) to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes A, B are joined by an edge if for some A ∈ A, B ∈ B A and B permute. We characterise those groups G for which
In this survey paper several subgroup embedding properties related to some types of permutability are introduced and studied.
We study finite groups in which every maximal subgroup is supersoluble or normal. Our results answer some questions arising from papers of Asaad and Rose.
Article history: Received 20 December 2012 Received in revised form 12 December 2013 Accepted 14 January 2014 Communicated by R. van Glabbeek