Search results for "Simple group"
showing 7 items of 37 documents
Uncountable existentially closed groups in locally finite group classes
1990
In this paper, will always denote a local class of locally finite groups, which is closed with respect to subgroups, homomorphic images, extensions, and with respect to cartesian powers of finite -groups. Examples for x are the classes L ℐπ of all locally finite π-groups and L(ℐπ ∩ ) of all locally soluble π-groups (where π is a fixed set of primes). In [4], a wreath product construction was used in the study of existentially closed -groups (=e.c. -groups); the restrictive type of construction available in [4] permitted results for only countable groups. This drawback was then removed partially in [5] with the help of permutational products. Nevertheless, the techniques essentially only per…
A reduction theorem for the Galois–McKay conjecture
2020
We introduce H {\mathcal {H}} -triples and a partial order relation on them, generalizing the theory of ordering character triples developed by Navarro and Späth. This generalization takes into account the action of Galois automorphisms on characters and, together with previous results of Ladisch and Turull, allows us to reduce the Galois–McKay conjecture to a question about simple groups.
A character-theory-free characterization of the Mathieu group M12
1990
AbstractThe known characterization of the Mathieu group M12 by the structure of the centralizer of a 2-central involution is based on the application of the theory of exceptional characters and uses in addition a block theoretic result which asserts that a simple group of order |M12| is isomorphic to M12. The details of the proof of the latter result had never been published. We show here that M12 can be handled in a completely elementary and group theoretical way.
The simple groups related to M24, II
1973
The objective of this paper is to prove the following generalization of the main result in [2]: THeorem. Let G be a finite simple group which possesses an involution t such that the centralizer of t in G is isomorphic to the centralizer of an involution in H. Then G is isomorphic to L5(2), M24, or H.
On second minimal subgroups of Sylow subgroups of finite groups
2011
A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids its chief factors. Partial cover and avoidance property has turned out to be very useful to clear up the group structure. In this paper, finite groups in which the second minimal subgroups of their Sylow p-subgroups, p a fixed prime, are partial CAP-subgroups are completely classified.
Characterization of strong chain geometries by their automorphism group
1992
A wide class of chain geometries is characterized by their automorphism group using properties of a distinguished involution.
A Gaschütz–Lubeseder Type Theorem in a Class of Locally Finite Groups
1999
The aim of this paper is to present a Gaschutz–Lubeseder type theorem in the class cL of all radical locally finite groups satisfying min−p for all primes p. Notice that these groups are countable and co-Hopfian by [1, (5.4.8)]. In retrospect, the theory of saturated formations of finite soluble groups began with the results of Gaschutz [3] in 1963. He introduced the concept of “covering subgroup” as a generalization of Sylow and Hall subgroups. These covering subgroups have many of the properties of Sylow and Hall subgroups other than the arithmetic ones. The main idea of Gaschutz’s work was concerned with group theoretical classes having the same properties. He defined a formation F to be…