groups of infinite rank in which every subgroup is either normal or self-normalizing are characterized in terms of their subgroups of infinite rank.

We discuss algebraic and analytic structure of rational Lax operators. With algebraic reductions of Lax equations we associate a reduction group-a group of twisted automor-phisms of the corresponding infinite dimensional Lie algebra. We present a complete study of dihedral reductions for sl(2, C) Lax operators with simple poles and corresponding integrable equations. In the last section we give...

Abstract Let G be a group and $$G_0 \subseteq G$$ G 0 ⊆ subset. A sequence over $$G_0$$ means finite of terms from , where the order elements is disregarded repetition allowed. product-one whose can ordered such that their product...

IT is well known that every group which contains at least one operator of order 2 must contain an odd number of such operators and that there is an infinite number of groups such that each of them contains exactly 2m + 1 operators of order 2, where m is an arbitrary positive integer or 0. It is also known that if exactly one half of the operators of a group are of order 2 then the order of this...

In the structure of the the title compound, C(13)H(9)Cl(2)NO, the N-H and C=O groups are mutually trans. Furthermore, the conformation of the C=O group is syn to the ortho-chloro group in the benzoyl ring, while the N-H bond is anti to the meta-chloro group in the aniline ring. The amide group forms dihedral angles of 89.11 (19) and 22.58 (37)°, respectively, with the benzoyl and aniline rings,...

Classifying integral graphs is a hard problem that initiated by Harary and Schwenk in 1974. In this paper, with the help of character table, we treat corresponding for Cayley over semi-dihedral group SD8n = ?a,b | a4n b2 1; bab a2n-1?, n ? 2. We present several necessary sufficient conditions integrality SD8n, also obtain some simple terms Boolean algebra hai. particular, give groups SD2n (n?4)...

in this paper we classify fuzzy subgroups of the dihedral group $d_{pqrs}$  for distinct primes  $p$, $q$, $r$ and $s$. this follows similar work we have done on distinct fuzzy subgroups of some dihedral groups.we present formulae for the number of (i) distinct maximal chains of subgroups, (ii) distinct fuzzy subgroups and (iii) non-isomorphic classes of fuzzy subgroups under our chosen equival...