Beltrán, Antonio; Felipe Román, María Josefa; Shao, Changguo(Springer Verlag (Germany), 2015-10)

We prove an extension of the renowned Itô’s theorem on groups having two class sizes in three different directions at the same time: normal subgroups, p′p′-elements and prime-power order elements. Let NN be a normal subgroup ...

Beltrán, Antonio; Felipe, María José; Melchor, Carmen(University of Isfahan, 2018)

[EN] We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework ...

Beltrán, Antonio; Felipe Román, María Josefa; Melchor, Carmen(Elsevier, 2015-12-01)

Let G be a finite group and let N be a normal subgroup of G.
We attach to N two graphs ΓG(N) and Γ∗
G(N) related to the
conjugacy classes of G contained in N and to the set of primes
dividing the sizes of these classes, ...

Beltrán, Antonio; Felipe Román, María Josefa; Shao, Changguo(De Gruyter, 2015-01)

. Let N be a normal subgroup of a group G and let p be a prime. We prove that if
the p-part of jx
Gj is a constant for every prime-power order element x 2 N n Z.N /, then
N is solvable and has normal p-complement.

Beltrán, Antonio; Felipe Román, María Josefa(Springer Verlag (Germany), 2014-12)

Given a finite group G which possesses a non-abelian simple normal subgroup N having exactly four G-class sizes, we prove that N is isomorphic to PSL(2,2a) with a≥2. Thus, we obtain an extension for normal subgroups of the ...

Akhlaghi, Z.; Beltrán, Antonio; Felipe Román, María Josefa; Khatami, M.(Springer Verlag (Germany), 2012-07)

Let G be a finite group and N be a normal subgroup of G. Suppose that the set of G-conjugacy class sizes of N is {1, m, n}, with m < n and m does not divide n. In this paper, we show that N is solvable, and we determine ...

Beltrán, Antonio; Felipe Román, María Josefa; Melchor, Carmen(Springer-Verlag, 2017-01)

[EN] Let G be a finite group and N a normal subgroup of G. We determine the
structure of N when the graph G(N), which is the graph associated to the conjugacy
classes of G contained in N, has no triangles and when the graph ...