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 ...
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(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 ...
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 ...