1,720,974 research outputs found
A new characteristic subgroup for pushing up I
No full textLet T be a finite p-group. In this paper we introduce a new characteristic subgroup W(T) of T containing Z(T). This subgroup allows to give the structure of p-minimal finite groups G of characteristic p with PSL2(pn)-factor group which satisfy Z(T) G and W(T) G. This result generalizes a classical pushing up result obtained by Baumann [1] (for p = 2) and Niles [8]
p-Groups of Small Breadth
No full textIn this paper we give a characterization of p-groups of breadth 2 for all primes and of breadth 3 for p odd
Baumann-components of finite groups of characteristic p, reduction theorems
No full textWe continue the project started in "Baumann-components of finite groups of characteristic p, general theory" to describe the structure of the finite groups G of characteristic p in terms of their Baumann components and the conjugacy class Baup(G). The reduction theorem proved in that paper allows to assume that G has a unique Baumann component. In this paper we use this property to determine the isomorphism type of G/Op(G) and the action of G on Ω1(Z(Op(G))). In addition, we prove reduction theorems which allow to focus on groups G which satisfy G/Op(G)≅SLn(q), Sp2n(q) or G2(q) and Op(G)⩽B for B∈Baup(G)
Baumann-components of finite groups of characteristic p, the W(B)-theorem
No full textThis paper completes the investigation of finite CK-groups of characteristic p in terms of their Baumann components we began in [Baumann-components of finite groups in characteristic p, general theory] and [Baumann-components of finite groups in characteristic p, reduction theorems]. In this paper we define for each finite p-group B a non-trivial characteristic subgroup W(B) and for each finite CK-group G of characteristic p with B in Baup(G), subnormal subgroups of G called Baumann blocks of G. We prove that G = N_G(W(B))E_W(G), where E_W(G) is the normal subgroup generated by the Baumann blocks of G. Moreover, we give the exact structure of the Baumann blocks of G and show that any two distinct Baumann blocks centralize each other
Baumann-components of finite groups of characteristic p, general theory
No full textIn this paper we introduce a new conjugacy class Bau_p(G) of p-subgroups of finite groups G of characteristic p. We then prove some factorization and decomposition theorems related to this conjugacy class. In particular, these results show that the only obstructions for B∈Bau_p(G) being normal in G are the Baumann components of G, a class of subnormal subgroups E with E/Op(E) quasisimple or SL2(p)′ for p≤3
The P!-Theorem
No full textIn this paper we prove a result that is used in the investigation of finite K_p-groups of local characteristic p. More precisely, we show that one of the cases given in the "Structure Theorem" by Meierfrankenfeld, Stellmacher and Stroth does not occur
The !-theorem
No full textIn this paper we prove a result that is used in the investigation of finite K_p-groups of local characteristic p. It is part of an attempt to revise a major part of the classification of the finite simple groups. A description of this program can be found in [U.Meierfrankenfeld, B.Stellmacher, G.Stroth, "Finite groups of local characteristic p: an overview", Groups, Combinatorics and Geometry, Durham, 2001 (World Scientific Publishing, River Edge, NJ, 2003) pp. 155-192]
The -Theorem
No full textThe paper under review is part of an ongoing project to give a proof for large parts of the classification of the finite simple groups which is different from the existing one. Moreover, the authors prove some result which is of independent interest.\par They consider the usual amalgam set up, i.e., two groups which are of characteristic -type, share a common Sylow -subgroup but no nontrivial normal subgroup of . Now the special assumptions are (i) , , (ii) There is with , , , or () and is the natural module, . (iii) or and or ; (iv) There is a 2-dimensional singular subspace in such that , .\par Then the authors show that this setup does just occur in very special situations. Either , and or , or or , or and , and and are natural -modules dual to each other.\par This result is similar to the result due to {\it B. Stellmacher} and {\it F. G. Timmesfeld} [Mem. Am. Math. Soc. 649 (1998; Zbl 0911.20024)] but does not follow from that result. This is now used to get a technical result, the -theorem. This under certain assumptions, which are technical, says basically the following. Let be a group with , , of local characteristic , and be a maximal -local containing . As the generic simple group of local characteristic is a group of Lie type over a field of characteristic , the aim is to get a geometry for . In this sense then is a maximal parabolic. Now, the authors consider a minimal parabolic . Under a further technical assumption, they show that there is a unique minimal parabolic containing , which does not normalize or there is one of the exceptions described by the theorem above. Further, they show that the group generated by and is a rank 2 Lie group. So if induces a Lie group this result provides us with a building geometry for .
[Gernot Stroth (Halle)
General offender theory
No full textWe present an offender theory that is symmetric in offender and offended group and also a replacement theorem that does not need that the groups in question are abelian. We then use this theory to define variations of Thompson and Baumann subgroups and prove a general Baumann argument. (C) 2017 Elsevier Inc. All rights reserved
Transitive permutation groups with cyclic point stabilizers of maximum order
No full textThe purpose of this paper is to classify transitive permutation groups where the stabiliser is cyclic of order where the degree is . This is a continuation of a paper by {\it A. Lucchini} [Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 9, No. 4, 241-243 (1998; Zbl 0940.20006)]. However the main result is more general, Theorem: Let be a finite group and let be a set of primes dividing the order of . Assume that has an Abelian Hall -subgroup, . Then one of the following hold: (a) , (b) , or (c) where each is a -transitive Frobenius group whose complement is a -group.\par The question arose from a paper by {\it L. Babai}, {\it A. J. Goodman} and {\it L. Pyber} [J. Algebra 195, No. 1, 1-29 (1997; Zbl 0886.20020)].
[Alan R. Camina (Norwich)
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