0000000000388043
AUTHOR
M. J. Iranzo
showing 5 related works from this author
A conjecture on the number of conjugacy classes in ap-solvable group
1996
IfG is ap-solvable group, it is conjectured that k(G/O P (G) ≤ |G| p ′. The conjecture is easily obtained for solvable groups as a consequence of R. Knorr’s work on the k(GV) problem. Also, a related result is obtained: k(G/F(G)) is bounded by the index of a nilpotent injector ofG.
Product of nilpotent subgroups
2000
We will say that a subgroup X of G satisfies property C in G if \({\rm C}_{G}(X\cap X^{{g}})\leqq X\cap X^{{g}}\) for all \({g}\in G\). We obtain that if X is a nilpotent subgroup satisfying property C in G, then XF(G) is nilpotent. As consequence it follows that if \(N\triangleleft G\) is nilpotent and X is a nilpotent subgroup of G then \(C_G(N\cap X)\leqq X\) implies that NX is nilpotent.¶We investigate the relationship between the maximal nilpotent subgroups satisfying property C and the nilpotent injectors in a finite group.
Fitting classes ℱ such that all finite groups have ℱ-injectors
1986
Let ℱ be an homomorph and Fitting class such thatEzℱ=ℱ. In this paper we prove that if all ℱ-constrained groups have ℱ-injectors, then all groups have ℱ-injectors. In particular if ℱ is a class of quasinilpotent groups containing the nilpotent groups, then every group has ℱ-injectors.
A class of finite groups having nilpotent injectors
1986
AbstractThe purpose of this paper is to construct a class of groups which properly contains the class of N-constrained groups, and which is such that all groups in this class have N-injectors.
ARITHMETICAL QUESTIONS IN π-SEPARABLE GROUPS
2005
If G is a finite π-separable group, π a set of primes und X is a π-suhgroup of G, let vπ(G, X) be the number of Hall π-suhgroups of G containing X. If K is a subgroup of G containing X, we prove that vπ(K,X) divides vπ(G).