On 2-closures of rank 3 groups
نویسندگان
چکیده
A permutation group G on ? is called a rank 3 if it has precisely three orbits in its induced action × . The largest having the same as 2 - closure of description -closures groups given. As special case, proved that -closure primitive one-dimensional affine sufficiently large degree also and one-dimensional.
منابع مشابه
COUNTING DISTINCT FUZZY SUBGROUPS OF SOME RANK-3 ABELIAN GROUPS
In this paper we classify fuzzy subgroups of a rank-3 abelian group $G = mathbb{Z}_{p^n} + mathbb{Z}_p + mathbb{Z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...
متن کاملOn imprimitive rank 3 permutation groups
A classification is given of rank 3 group actions which are quasiprimitive but not primitive. There are two infinite families and a finite number of individual imprimitive examples. When combined with earlier work of Bannai, Kantor, Liebler, Liebeck and Saxl, this yields a classification of all quasiprimitive rank 3 permutation groups. Our classification is achieved by first classifying imprimi...
متن کاملActions of groups of finite Morley rank on abelian groups of rank 2
We classify actions of groups of finite Morley rank on abelian groups of Morley rank 2: there are essentially two, namely the natural actions of SL(V ) and GL(V ) with V a vector space of dimension 2.
متن کاملRank 3 Groups and Biplanes
Let G be a primitive rank 3 permutation group on a set X in which r(x) is a nontrivial G,-orbit, with II = I X 1, u = I I’(X)]. Tsuzuku [27] showed that, if G, acts as the symmetric group on r(x), then (v, n) = (2, 5), (3, lo), (5, 16), or (7, 50); he determined the possible groups in each case. Bannai [2] obtained essentially the same result under the assumption G, is 4-transitive on F(x). (Of...
متن کاملcounting distinct fuzzy subgroups of some rank-3 abelian groups
in this paper we classify fuzzy subgroups of a rank-3 abelian group $g = mathbb{z}_{p^n} + mathbb{z}_p + mathbb{z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. we present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...
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: Ars Mathematica Contemporanea
سال: 2021
ISSN: ['1855-3974', '1855-3966']
DOI: https://doi.org/10.26493/1855-3974.2450.1dc