Nilpotent injectors in minimal simple groups
نویسندگان
چکیده
منابع مشابه
Minimal Permutation Representations of Nilpotent Groups
A minimal permutation representation of a finite group G is a faithful G-set with the smallest possible size. We study the structure of such representations and show that for certain groups they may be obtained by a greedy construction. In these situations (except when central involutions intervene) all minimal permutation representations have the same set of orbit sizes. Using the same ideas w...
متن کاملMinimal Geodesics and Nilpotent Fundamental Groups
Hedlund 18] constructed Riemannian metrics on n-tori, n 3 for which minimal geodesics are very rare. In this paper we construct similar examples for every nilpotent fundamental group. These examples show that Bangert's existence results of minimal geodesics 4] are optimal for nilpotent fundamental groups.
متن کاملOn minimal degrees of faithful quasi-permutation representations of nilpotent groups
By a quasi-permutation matrix, we mean a square non-singular matrix over the complex field with non-negative integral trace....
متن کاملNilpotent injectors in Finite Groups All of Whose Local Subgroups Are M-Constrained
Nilpotent injectors have the property that they contain every nilpotent subgroup that they normalize. A. Bialostocki has conjectured [4] that if G is a finite group then all nilpotent injectors of G are conjugate. He has verified his conjecture for the symmetric and alternating groups. The conjecture is also true for soluble groups. The only property of soluble groups used in proving this is C(...
متن کاملDefinably Simple Groups in O-minimal Structures
Let G = 〈G, ·〉 be a group definable in an o-minimal structure M. A subset H of G is G-definable if H is definable in the structure 〈G, ·〉 (while definable means definable in the structure M). Assume G has no Gdefinable proper subgroup of finite index. In this paper we prove that if G has no nontrivial abelian normal subgroup, then G is the direct product of G-definable subgroups H1, . . . ,Hk s...
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: Journal of Algebra
سال: 2012
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2012.03.031