The study aims to establish relationships between subgroup properties and specific group invariants.
Defined the invariant λ(G) for finite groups.
Analyzed the relationship between λ(G) and group properties such as order and exponent.
Developed mathematical bounds based on derived length.
Established upper and lower bounds on the order of groups based on λ(G).
Demonstrated how the exponent of groups relates to λ(G).
Provided insights into the implications of derived length for subgroup structures.
Resumen
Abstract Let (G) be the maximum number of subgroups in an irredundant cover of the finite group G. We establish bounds on the order, exponent and derived length of the group in terms of this invariant.
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On Maximal Cyclic Subgroups of Finite Groups | Synapse