On quantitative structure of small Ree groups
نویسندگان
چکیده
منابع مشابه
The Mobius function of the small Ree groups
The Möbius function for a group G was introduced in 1936 by Hall in order to count ordered generating sets of G. In this paper we determine the Möbius function of the simple small Ree groups, R(q) = G2(q) where q = 3 for m > 0, using their 2-transitive permutation representation of degree q + 1. We also describe their maximal subgroups in terms of this representation. We use this to enumerate s...
متن کاملRecognising the small Ree groups in their natural representations
We present Las Vegas algorithms for constructive recognition and constructive membership testing of the Ree groups G2(q) = Ree(q), where q = 3 for some m > 0, in their natural representations of degree 7. The input is a generating set X ⊂ GL(7, q). The constructive recognition algorithm is polynomial time given a discrete logarithm oracle. The constructive membership testing consists of a prepr...
متن کاملthe structure of lie derivations on c*-algebras
نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
15 صفحه اولGroups of Ree type in characteristic 3 acting on polytopes
Every Ree group R(q), with q 6= 3 an odd power of 3, is the automorphism group of an abstract regular polytope, and any such polytope is necessarily a regular polyhedron (a map on a surface). However, an almost simple group G with R(q) < G ≤ Aut(R(q)) is not a C-group and therefore not the automorphism group of an abstract regular polytope of any rank.
متن کاملOn the simple groups of Suzuki and Ree
We develop a new and uniform approach to the three families of simple groups of Lie type discovered by Suzuki and Ree, without using Lie algebras. A novel type of algebraic structure is defined, whose automorphism groups are the groups in question. This leads to elementary proofs of the group orders and simplicity, as well as much information on subgroup structure and geometry.
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2016
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2016.1260730