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A Menon-type identity using Klee's function

Arya Chandran, Neha Elizabeth Thomas, K. Vishnu Namboothiri (2022)

Czechoslovak Mathematical Journal

Menon’s identity is a classical identity involving gcd sums and the Euler totient function φ . A natural generalization of φ is the Klee’s function Φ s . We derive a Menon-type identity using Klee’s function and a generalization of the gcd function. This identity generalizes an identity given by Y. Li and D. Kim (2017).

Active sums I.

J. Alejandro Díaz-Barriga, Francisco González-Acuña, Francisco Marmolejo, Leopoldo Román (2004)

Revista Matemática Complutense

Given a generating family F of subgroups of a group G closed under conjugation and with partial order compatible with inclusion, a new group S can be constructed, taking into account the multiplication in the subgroups and their mutual actions given by conjugation. The group S is called the active sum of F, has G as a homomorph and is such that S/Z(S) ≅ G/Z(G) where Z denotes the center.The basic question we investigate in this paper is: when is the active sum S of the family F isomorphic to the...

Characterization by intersection graph of some families of finite nonsimple groups

Hossein Shahsavari, Behrooz Khosravi (2021)

Czechoslovak Mathematical Journal

For a finite group G , Γ ( G ) , the intersection graph of G , is a simple graph whose vertices are all nontrivial proper subgroups of G and two distinct vertices H and K are adjacent when H K 1 . In this paper, we classify all finite nonsimple groups whose intersection graphs have a leaf and also we discuss the characterizability of them using their intersection graphs.

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