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...

A pair of non-empty subsets (W,W?) in an abelian group G is additive complement if W+W?=G. The set W? said to be minimal W W+(W??{w?})?G,?w??W?. In general, given arbitrary subset a group, the existence complement(s) depends on its structure. dual problem asks that such set, it some subset. Additive complements have been studied context representations integers since time Erd?s, Hanani, Lorentz...

We give another proof of an observation of Thévenaz [4] and present a fusion system version of it. Namely, for a saturated fusion system F on a finite p-group S, we show that the number of the F-conjugacy classes of cyclic subgroups of S is equal to the rank of certain square matrices of numbers of orbits, coming from characteristic bisets, the characteristic idempotent and finite groups realiz...

Current strategies for the control of schistosomiasis are based primarily on chemotherapy but successful vaccination against infection has been also demonstrated in several host parasitic models. The present study was designed to assess the effect of vaccination with schistosomulae atte nuated by different doses of γ-radiation in mice challenged with S. mansoni cercariae regarding hepatic histo...

For a compact surface $S = S_{g,n}$ with $3g + n \geq 4$, we introduce family of unitary representations the mapping class group Mod($S$) based on space measured foliations. this representations, show that none them has almost invariant vectors. As one application, obtain an inequality concerning action Teichmuller $S$. Moreover, using same method plus recent results about weak equivalence, als...

Given a set S, we show that there is a strict relation between the notion of similarity on S and the one of fuzzy subgroup of transformations in S . Such a relation enables us to extablish a connection between fuzzy subgroups and distances.

We prove that a parabolic subgroup P P contained in another P prime"> ′ encoding="application/x...

Let S be an orientable surface. Let Diff(S) be the group of all diffeomorphisms of S, and Diff(S) its identity component. Then Mod±S = Diff(S)/Diff (S) is called the extended mapping class group or the extended Teichmüller modular group of S. Let Diff(S) be the subgroup of orientation preserving diffeomorphisms of S. Then Mod(S) = Diff(S)/Diff(S) is called the mapping class group or the Teichmü...