Papers by L. Ortiz de Elguea
Let |G| = p a1 1 ...p at t be the prime power factorization of the order of a finite group G, let... more Let |G| = p a1 1 ...p at t be the prime power factorization of the order of a finite group G, let r(G) be the number of conjugacy classes and set d |G| := gcd(p 1 − 1, ..., p t − 1) and δ |G| := gcd(p 1 2 − 1, ..., p 2 t − 1). The aim of the paper is to give elementary proofs of the congruences |G| ≡ r(G)(modδ |G|) and |G| ≡ r(G)(modd 2 |B|). MSC: 20D60 Arithmetic and combinatorial problems involving abstract finite groups
A. VERA L6PEZ and L. ORTIZ DE ELGUEA ARCH. MATH. Finally, if G is an X~-group and H is a Hall n-s... more A. VERA L6PEZ and L. ORTIZ DE ELGUEA ARCH. MATH. Finally, if G is an X~-group and H is a Hall n-subgroup of G satisfying: r(H) IHI-IH[ 2 (mod 2 eGt~) 9 d (]G[) 9 ([G[)), then we say that G is an Y~-group. In particular, groups containing an abelian Hall n-subgroup are Y~-groups. The purpose in Section 2, is to make an investigation about the number v~ (G), when G is an X.-group. In this case, the following congruence holds: v~(G) = 1 (mod ~,(IGI)). This result improves those of J. S. Clowes, given in [2]. Let G be an L~-group and let H be a Hall n-subgroup of G, then r G (C G (H)) is the number of conjugacy classes whose cardinal is a n'-number and r G (H) is the number of conjugacy classes of 7z-elements of G. In Section 3 the following congruences are shown: A) If G is L~-group, then rG(CG(H)) = ICG(H)I (rood d(IGI) #~(IGI)). B) If G is X~-group, then ra(H)-IHI (mod d(lGI)2). Further, if H is abelian, the following congruence holds: rG(n)-Inl (rood d(Ial) " ~(Ial)). 2. The number v~ (G).
de la forma más "simple" posible, simultáneamente. El problema principal a tratar en este libro e... more de la forma más "simple" posible, simultáneamente. El problema principal a tratar en este libro es cómo elegir dichas bases B c en V y B c en W. Curiosamente la solución aportada no es de naturaleza geométrica, como se verá. Obsérvese que si g = dim(Ker A∩Ker B), podemos elegir una base {e 1 ,. .. , e g } de Ker A ∩ Ker B, que se puede ampliar hasta una base
Hall p-subgroups and conjugacy classes
Arch Math, 1990
The conjugacy-vectors of all relative holomorphs of an elementary abelian group of order 16
Portugaliae Mathematica
Linear Algebra and its Applications, 1996
Let Ai, Bj (i = 1,2) be mi X ni complex matrices. We give a criterion for the regularity of the p... more Let Ai, Bj (i = 1,2) be mi X ni complex matrices. We give a criterion for the regularity of the pencil AA, @ A,-B, @ B,, and obtain the Weierstrass-Kronecker
Hall ?-subgroups and conjugacy classes
Archiv der Mathematik, 1990
On the number of conjugacy classes of a finite group modulo the greatest possible number
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Papers by L. Ortiz de Elguea