On some commutativity theorems for finite rings and finite groups
On some completeness properties for lattice ordered groups
On some elementary properties of soluble groups of derived length 2.
On some extrem properties of a class of simple groupoids.
On some finite 2-groups in which the derived group has two generators
We show that any finite 2-group, whose abelianization has either 4-rank at most 2 or 8-rank 0 and whose commutator subgroup is generated by two elements, is metabelian. We also prove that the minimal order of any 2-group with nonabelian commutator subgroup of 2-rank 2 is .
On Some Finite 2-Groups of Deficiency Zero
On some finite groupoids with distributive subgroupoid lattices
The aim of the paper is to show that if S(G) is distributive, and also G satisfies some additional condition, then the union of any two subgroupoids of G is also a subgroupoid (intuitively, G has to be in some sense a unary algebra).
On some finiteness conditions in semigroup and group theory.
On some flag-transitive non-classical -geometries. II.
On some free semigroups, generated by matrices
Let We call a complex number “semigroup free“ if the semigroup generated by and is free and “free” if the group generated by and is free. First families of semigroup free ’s were described by J. L. Brenner, A. Charnow (1978). In this paper we enlarge the set of known semigroup free ’s. To do it, we use a new version of “Ping-Pong Lemma” for semigroups embeddable in groups. At the end we present most of the known results related to semigroup free and free numbers in a common picture....
On Some Fully Invariant Subgroups of Summable Groups
We show the inheritance of summable property for certain fully invariant subgroups by the whole group and vice versa. The results are somewhat parallel to these due to Linton (Mich. Math. J., 1975) and Linton-Megibben (Proc. Amer. Math. Soc., 1977). They also generalize recent assertions of ours in (Alg. Colloq., 2009) and (Bull. Allah. Math. Soc., 2008)
On some geometric aspects of Bruhat orderings. I. A finer decomposition of Bruhat cells.
On some groups with almost regular element of prime order.
On some infinite dimensional linear groups
Let F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dimF(B/CoreG(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.
On some interpolation rules for lattice ordered groups
Let be an infinite cardinal. In this paper we define an interpolation rule for lattice ordered groups. We denote by the class of all lattice ordered groups satisfying , and prove that is a radical class.
On some Jordan-Hölder-Dedekind type theorems in lattices.
On some maximal -quasinormal subgroups of finite groups.
On some metabelian 2-groups and applications I
Let G be some metabelian 2-group satisfying the condition G/G’ ≃ ℤ/2ℤ × ℤ/2ℤ × ℤ/2ℤ. In this paper, we construct all the subgroups of G of index 2 or 4, we give the abelianization types of these subgroups and we compute the kernel of the transfer map. Then we apply these results to study the capitulation problem for the 2-ideal classes of some fields k satisfying the condition , where is the second Hilbert 2-class field of k.
On some model theoretic problems concerning certain extensions of abelian groups by groups of finite exponent
On some non-rational congruences on free commutative semigroups.