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; SHAO, CHANG GUO(World Scientific Publishing, 2012-12)
The authors have realized that in the proof of Theorem 6 of [1] there is a mistake
although the conclusion of the theorem is correct. The proof of the theorem is
divided into two cases: when there exist no p-elements of ...
Beltrán, Antonio; Felipe Román, María Josefa(John Wiley & Sons, 2021-09)
[EN] Let G be a finite group and let K=xG be the conjugacy class of an element x of G. In this paper, it is proved that if N is a normal subgroup of G such that the coset xN is the union of K and K-1 (the conjugacy class ...
Beltrán, Antonio; Felipe Román, María Josefa(Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2011-03-18)
We determine the structure of all finite groups with four class sizes when two of them are coprime numbers larger than 1. We prove that such groups are solvable and that the set of class sizes is exactly {1, m, n, mk}, ...
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, ...
Alemany Martínez, Elena; Beltrán, Antonio; Felipe Román, María Josefa(Cambridge University Press, 2012)
Let G be a finite p-solvable group. We prove that if G has exactly two conjugacy class sizes of p'-elements of prime power order, say 1 and m, then m = p(a)q(b), for two distinct primes p and q, and G either has an abelian ...
Beltrán, Antonio; Felipe Román, María José; Melchor, Carmen(Springer-Verlag, 2018-08)
[EN] Suppose that G is a finite group and K is a non-trivial conjugacy class of G such that KK (-1) = 1 a D a D (-1) with D a conjugacy class of G. We prove that G is not a non-abelian simple group and we give arithmetical ...
Beltrán, Antonio; Felipe Román, María José(American Mathematical Society, 2012)
[EN] If G is a finite group and N is a normal subgroup of G with two C-conjugacy class sizes of elements of prime power order, then we show that N is nilpotent.
Beltrán, Antonio; Felipe Román, María Josefa(World Scientific Publishing, 2012-04)
It is shown that if the set of conjugacy class sizes of a finite group G is {1,m,n,mn}, where m, n are positive integers which do not divide each other, then G is up to central factors a {p,q}-group. In particular, G is solvable.
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; Camina, Rachel Deborah; Felipe Román, María Josefa; Melchor, Carmen(Springer-Verlag, 2020-04)
[EN] The aim of this paper is to show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper was to show several results about solvability ...
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 ...
Beltrán, Antonio; Felipe Román, María Josefa(Debreceni egyetem matematika intézet, 2013)
[EN] We study the solvability of a normal subgroup N of a finite group G having exactly three G-conjugacy class sizes. We show that if the set of G-class sizes of N is {1, m, mpa
}, with p a prime not dividing m, then N ...
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(Springer Verlag (Germany), 2013-08)
Let G be a finite p-solvable group for some prime p and suppose that the set of p-regular conjugacy class sizes is {1,m,mn} with (m,n)=1 and m coprime to p. We show that m=qb for some prime q and we describe the structure ...
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 ...