Structure of a Munn semigroup of finite rank every stable order of which is fundamental or antifundamental

We describe the structure of a Munn semigroup of finite rank every stable order of which is fundamental or antifundamental. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 1, pp. 52–60, January, 2009.     

On maximal stable orders on an inverse semigroup of finite rank with zero

We consider maximal stable orders on semigroups that belong to a certain class of inverse semigroups of finite rank. Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 8, pp. 1035–1041, August, 2008.     

Structure of a finite commutative inverse semigroup and a finite bundle for which the inverse monoid of local automorphisms is permutable

For a semigroup S, the set of all isomorphisms between the subsemigroups of the semigroup S with respect to composition is an inverse monoid denoted by PA(S) and called the monoid of local automorphisms of the semigroup S. The semigroup S is called permutable if, for any couple of congruences ρ and σ on S, we have ρ ∘ σ = σ ∘ ρ. We describe the structures of a finite commutative inverse semigroup and a finite bundle whose monoids of local automorphisms are permutable.     

Burnside algebra of a finite inverse semigroup

The Burnside algebra for a finite inverse semigroup over a field is considered (the analog of the Grothendieck algebra). The conditions for the algebra to be Frobenius are investigated. It is shown that, if all the subgroups in the semigroup are commutative, then its Burnside algebra is Frobenius if and only if the order of any maximal subgroup is not divisible by the square of the field characteristic.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 46, pp. 41–52, 1974.     

Groups in which every right order is two sided

These two authors thank the University of Indiana at South Bend (Summer Faculty Fellow-ship) and NSERC, Canada, respectively, for partial support.     

On nilpotent subsemigroups of a finite symmetrical inverse semigroup

This work was supported by the State Foundation for Fundamental Research of SCST of the Ukrain.     

Characterization of the semilattice of idempotents of a finite-rank permutable inverse semigroup with zero

We give a characterization of the semilattice of idempotents of a finite-rank permutable inverse semigroup with zero. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1353–1362, October, 2007.     

Finite groups in which every pair of elements of the same order is either conjugate or inverse-conjugate

For a group G, elements a and b are said to be inverse-conjugate if α is conjugate to b^?1. We classify all finite groups in which every pair of elements of the same order is either conjugate or inverse-conjugate. The groups with this property are either small soluble groups, which are explicitly listed, or the groups L ₂;(7), M₁₁, M₂₃ and Aut(Sz(8)).     

Finite groups in which every self-centralizing subgroup is nilpotent or subnormal or a TI-subgroup

Czechoslovak Mathematical Journal - Let G be a finite group. We prove that if every self-centralizing subgroup of G is nilpotent or subnormal or a TI-subgroup, then every subgroup of G is nilpotent...     

Finite groups in which every subgroup is a subnormal subgroup or a TI-subgroup

In this paper, we obtain a complete classification of finite groups in which every subgroup is a subnormal subgroup or a TI-subgroup.     

The rank of the inverse semigroup of partial automorphisms on a finite fence

Semigroup Forum - A fence is a particular partial order on a (finite) set, close to the linear order. In this paper, we calculate the rank of the semigroup $$\mathscr {FI}_{n}$$ of all...     

Center of the semigroup algebra of a finite inverse semigroup over the field of complex numbers

In the semigroup algebra A of a finite inverse semigroup S over the field of complex numbers to an indempotent e there is assigned the sum (e)=e+(–1)^Ke_L1e_iK, where e_i,...,e_m are maximal preidempotents of the idempotent e, and the summation goes over all nonempty subsets {i₁,...,i_k} of the set {1,...m} Then for any class K of conjugate group elements of the semigroup S the element K=a·(a^–1a) (the summation goes over all ag) is a central element of the algebra A, and the set {K} of all possible such elements is a basis for the center of the algebra A.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 74, pp. 154–158, 1978.     

Structure of a permutable Munn semigroup of finite rank

A semigroup any two congruences of which commute as binary relations is called a permutable semigroup. We describe the structure of a permutable Munn semigroup of finite rank. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 6, pp. 742–746, June, 2006.