In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

Let Jl consist of the groups GÍL m) = (a, b; a~ b a = b"1) where |/.| 4 1 4 |zzi|, lm40 and l, m are coprime. We characterize the endomorphisms of these groups, compute the centralizers of special elements and show that the endomorphism a —• a, b —' b is onto with a nontrivial fully invariant kernel. Hence G(l, m) is non-Hopfian in the'fully invariant sense.' Our purpose is to prove the results...

Let L be a simply-connected simple connected algebraic group over number field F, and H semisimple absolutely maximal F-subgroup of L. $$\Delta (H)$$ the image diagonally embedded in $$L^n$$ . Under cohomological condition, we prove an asymptotic formula for rational points bounded height on projective equivariant compactifications (H)\backslash L^n$$ with respect to balanced line bundle.

Given a class C of subgroups of a topological group G, we say that a subgroup H ∈ C is a universal C subgroup of G if every subgroup K ∈ C is a continuous homomorphic pre-image of H. Such subgroups may be regarded as complete members of C with respect to a natural pre-order on the set of subgroups of G. We show that for any locally compact Polish group G, the countable power G has a universal K...

The group AS is called an Artin group and relations sts . . . } {{ } ms,t terms = tst . . . } {{ } ms,t terms are called braid relations. For instance, if S = {s1, . . . , sn} with msi,sj = 3 for |i − j| = 1 and msi,sj = 2 otherwise, then the associated Artin group is the braid group. We denote by A+S the submonoid of AS generated by S. This monoid A+S has the same presentation as the group AS ...

Abstract We give technical conditions for a quasi-isometry of pairs to preserve subgroup being hyperbolically embedded. consider applications the and commensurability invariance acylindrical hyperbolicity finitely generated groups.

Let K ⊂ C be a field finitely generated over Q, K(a) ⊂ C the algebraic closure of K, G(K) = Gal(K(a)/K its Galois group. For each positive integer m we write K(μm) for the subfield of K(a) obtained by adjoining to K all mth roots of unity. For each prime l we write K(l) for the subfield of K(a) obtained by adjoining to K all l−power roots of unity. We write K(c) for the subfield of K(a) obtaine...

Note that the intersection property in Theorem A is equivalent to saying that NL(P ) is a p-group. Also, since this property is clearly independent of the choice of P in Sylp(G), it is clear that L is characteristic in G. Our interest in this characteristic subgroup was motivated by the following. Theorem B. Suppose that G is p-solvable and let L be the largest normal subgroup of G such that L∩...