On varieties of completely regular semigroups.
On varieties of completely regular semigroups II.
On varieties of completely regular semigroups III.
On varieties of Hilbert type
A variety over a field is of Hilbert type if is not thin. We prove that if is a dominant morphism of -varieties and both and all fibers , , are of Hilbert type, then so is . We apply this to answer a question of Serre on products of varieties and to generalize a result of Colliot-Thélène and Sansuc on algebraic groups.
On varieties of left distributive left idempotent groupoids
We describe a part of the lattice of subvarieties of left distributive left idempotent groupoids (i.e. those satisfying the identities x(yz) ≈ (xy)(xz) and (xx)y ≈ xy) modulo the lattice of subvarieties of left distributive idempotent groupoids. A free groupoid in a subvariety of LDLI groupoids satisfying an identity xⁿ ≈ x decomposes as the direct product of its largest idempotent factor and a cycle. Some properties of subdirectly ireducible LDLI groupoids are found.
On Varieties of Literally Idempotent Languages
A language L ⊆A* is literally idempotent in case that ua2v ∈ L if and only if uav ∈ L, for each u,v ∈ A*, a ∈ A. Varieties of literally idempotent languages result naturally by taking all literally idempotent languages in a classical (positive) variety or by considering a certain closure operator on classes of languages. We initiate the systematic study of such varieties. Various classes of literally idempotent languages can be characterized using syntactic methods. A starting example is the...
On varieties of regular -semigroups
On varieties of regular -semigroups, II
On Virtual Properties and Group Extensions.
On volumes of arithmetic quotients of
We apply G. Prasad’s volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of . As a result we prove that for any even dimension there exists a unique compact arithmetic hyperbolic -orbifold of the smallest volume. We give a formula for the Euler-Poincaré characteristic of the orbifolds and present an explicit description of their fundamental groups as the stabilizers of certain lattices in quadratic spaces. We...
On weakly commutative semigroups
On weakly -permutably embedded subgroups
Suppose is a finite group and is a subgroup of . is said to be -permutably embedded in if for each prime dividing , a Sylow -subgroup of is also a Sylow -subgroup of some -permutable subgroup of ; is called weakly -permutably embedded in if there are a subnormal subgroup of and an -permutably embedded subgroup of contained in such that and . We investigate the influence of weakly -permutably embedded subgroups on the -nilpotency and -supersolvability of finite...
On weakly-supplemented subgroups and the solvability of finite groups
A subgroup of a finite group is weakly-supplemented in if there exists a proper subgroup of such that . In this paper, some interesting results with weakly-supplemented minimal subgroups or Sylow subgroups of are obtained.
On weakly-supplemented subgroups of finite groups
A subgroup of a finite group is weakly-supplemented in if there exists a proper subgroup of such that . In this paper, some interesting results with weakly-supplemented minimal subgroups to a smaller subgroup of are obtained.
On -operators in an arbitrary semigroup
On zero free sets.
On zero-free subset sums
On zeros of characters of finite groups
For a finite group and a non-linear irreducible complex character of write . In this paper, we study the finite non-solvable groups such that consists of at most two conjugacy classes for all but one of the non-linear irreducible characters of . In particular, we characterize a class of finite solvable groups which are closely related to the above-mentioned question and are called solvable -groups. As a corollary, we answer Research Problem in [Y. Berkovich and L. Kazarin: Finite...
On zero-sum sequences in .
On zero-sum subsequences in finite Abelian groups.