Sharply 2-transitive groups
نویسندگان
چکیده
We give an explicit construction of sharply 2-transitive groups with fixed point free involutions and without nontrivial abelian normal subgroup.
منابع مشابه
Sharply 2-transitive sets of permutations and groups of affine projectivities
Using new results on sharply transitive subsets, we determine the groups of projectivities of finite affine planes, apart from (unknown) planes of order 23 or 24. The group of all projectivities of a geometry G is a measure for the complexity of G: this group tends to be rather large if G is far from being a classical geometry. See [PS81] for more information on the role of projectivities in ge...
متن کاملSharply $(n-2)$-transitive Sets of Permutations
Let $S_n$ be the symmetric group on the set $[n]={1, 2, ldots, n}$. For $gin S_n$ let $fix(g)$ denote the number of fixed points of $g$. A subset $S$ of $S_n$ is called $t$-emph{transitive} if for any two $t$-tuples $(x_1,x_2,ldots,x_t)$ and $(y_1,y_2,ldots ,y_t)$ of distinct elements of $[n]$, there exists $gin S$ such that $x_{i}^g=y_{i}$ for any $1leq ileq t$ and additionally $S$ is called e...
متن کاملSharply 2-transitive Groups with Point Stabilizer of Exponent 3 or 6
Using the fact that all groups of exponent 3 are nilpotent, we show that every sharply 2-transitive permutation group whose point stabilizer has exponent 3 or 6 is finite.
متن کاملSharply 2-transitive groups of projectivities in generalized polygons
The group of projectivities of (a line of) a projective plane is always 3-transitive. It is well known that the projective planes with a sharply 3-transitive group of projectivities are classi/ed: they are precisely the Pappian projective planes. It is also well known that the group of projectivities of a generalized polygon is 2-transitive. Here, we classify all generalized quadrangles, all /n...
متن کاملSharply 3-transitive groups
We construct the first sharply 3-transitive groups not arising from a near field, i.e. point stabilizers have no nontrivial abelian normal subgroup.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014