Finite Möbius-planes admitting a Zassenhaus group as group of automorphisms
نویسندگان
چکیده
منابع مشابه
Rank and order of a finite group admitting a Frobenius group of automorphisms
Suppose that a finite group G admits a Frobenius group of automorphisms FH of coprime order with kernel F and complement H. In the case where G is a finite p-group such that G = [G,F ] it is proved that the order of G is bounded above in terms of the order of H and the order of the fixed-point subgroup CG(H) of the complement, and the rank of G is bounded above in terms of |H| and the rank of C...
متن کاملFinite Möbius near-planes
We introduce finite Mobius near-planes of order n and show that these planes uniquely extend to Mobius planes of the same order if n ;:::: 5. Furthermore, Mobius near-planes of order n :s; 4 are discussed and the situation for the other two types of finite circle near-planes, Laguerre and Minkowski near-planes, is reviewed.
متن کاملFinite elation Laguerre planes admitting a two-transitive group on their set of generators
We investigate finite elation Laguerre planes admitting a group of automorphisms that is two-transitive on the set of generators. We exclude the sporadic cases of socles in two-transitive groups, as well as the cases with abelian socle (except for the smallest ones, where the Laguerre planes are Miquelian of order at most four). The remaining cases are dealt with in a separate paper. As a conse...
متن کاملSixteen-dimensional Locally Compact Translation Planes Admitting Sl2 H as a Group of Collineations
In this paper, all 16-dimensional locally compact translation planes admitting the unimodular quaternion group SL2H as a group of collineations will be determined explicitly. Besides the classical plane over the octonions there are a vast number of planes having this property, cf. the Classification Theorem (2.8). Indeed, the class of these planes covers an interesting borderline case: Among al...
متن کاملOn Marginal Automorphisms of a Group Fixing the Certain Subgroup
Let W be a variety of groups defined by a set W of laws and G be a finite p-group in W. The automorphism α of a group G is said to bea marginal automorphism (with respect to W), if for all x ∈ G, x−1α(x) ∈ W∗(G), where W∗(G) is the marginal subgroup of G. Let M,N be two normalsubgroups of G. By AutM(G), we mean the subgroup of Aut(G) consistingof all automorphisms which centralize G/M. AutN(G) ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1964
ISSN: 0019-2082
DOI: 10.1215/ijm/1256059457