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 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 ...
Akhlaghi, Zeinab; Beltrán Felip, Antonio; Felipe Román, María Josefa(Elsevier, 2014-02-01)
If G is a finite group, we show that any normal subgroup of G
which has exactly three G-conjugacy class sizes is solvable. Thus,
we give an extension for normal subgroups of the classical N. Itô’s
theorem which asserts ...
Akhlaghi, Zeinab; Beltrán Felip, Antonio; Felipe Román, María Josefa; Khatami, Maryam(Elsevier, 2011-06-15)
Let G be a finite p-solvable group and N be a normal subgroup of G. Suppose that the p-regular elements of N have exactly two G-conjugacy class sizes. In this paper it is shown that, if H is a p-complement of N, then either ...
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; 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 ...