منابع مشابه
groups of infinite rank with a normalizer condition on subgroups
groups of infinite rank in which every subgroup is either normal or self-normalizing are characterized in terms of their subgroups of infinite rank.
متن کاملCrystal bases and combinatorics of infinite rank quantum groups
The tensor powers of the vector representation associated to an infinite rank quantum group decompose into irreducible components with multiplicities independant of the infinite root system considered. Although the irreducible modules obtained in this way are not of highest weight, they admit a crystal basis and a canonical basis. This permits in particular to obtain for each familly of classic...
متن کاملgroups whose proper subgroups of infinite rank have polycyclic-by-finite conjugacy classes
a group g is said to be a (pf)c-group or to have polycyclic-by-finite conjugacy classes, if g/c_{g}(x^{g}) is a polycyclic-by-finite group for all xin g. this is a generalization of the familiar property of being an fc-group. de falco et al. (respectively, de giovanni and trombetti) studied groups whose proper subgroups of infinite rank have finite (respectively, polycyclic) conjugacy classes. ...
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 کاملSubgroups of Small Index in Infinite Symmetric Groups II
Throughout this paper Q will denote an infinite set, S:= Sym(Q) and G is a subgroup of S. If n: = |Q|, the cardinal of Q, then |.S| = 2". Working in ZFC, set theory with Axiom of Choice (AC), we shall be seeking the subgroups G with \S: G\ < 2". If A £ Q then S^ (respectively G{A}) denotes the setwise stabiliser of A in S (respectively in G); 5(A) and G(A) denote pointwise stabilisers; we ident...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1990
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1990-0963246-8