On minimal models in integral homotopy theory.
On minimal non CC-groups.
In this work it is shown that a locally graded minimal non CC-group G has an epimorphic image which is a minimal non FC-group and there is no element in G whose centralizer is nilpotent-by-Chernikov. Furthermore Theorem 3 shows that in a locally nilpotent p-group which is a minimal non FC-group, the hypercentral and hypocentral lengths of proper subgroups are bounded.
On minimal non-PC-groups
A group is said to be a PC-group, if is a polycyclic-by-finite group for all . A minimal non-PC-group is a group which is not a PC-group but all of whose proper subgroups are PC-groups. Our main result is that a minimal non-PC-group having a non-trivial finite factor group is a finite cyclic extension of a divisible abelian group of finite rank.
On minimal non-supersoluble groups.
On minimal permutation representations of classical simple groups.
On minimal subgroups which are normal.
On minimization theorems for polyadic groups H-derived from groups
On modular elements of the lattice of semigroup varieties
A semigroup variety is called modular if it is a modular element of the lattice of all semigroup varieties. We obtain a strong necessary condition for a semigroup variety to be modular. In particular, we prove that every modular nil-variety may be given by 0-reduced identities and substitutive identities only. (An identity is called substitutive if the words and depend on the same letters and may be obtained from by renaming of letters.) We completely determine all commutative modular...
On Modular Law for Ternary -Groupoids
On modular projective representations of finite nilpotent groups
Our aim is to determine necessary and sufficient conditions for a finite nilpotent group to have a faithful irreducible projective representation over a field of characteristic p ≥ 0.
On modules over the Hecke algebra of a p-adic group.
On monoids over which all strongly flat cyclic right acts are projective.
On monomial groups.
On monomial p...-representations of finite p-groups.
On Moufang A-loops
In a series of papers from the 1940’s and 1950’s, R.H. Bruck and L.J. Paige developed a provocative line of research detailing the similarities between two important classes of loops: the diassociative A-loops and the Moufang loops ([1]). Though they did not publish any classification theorems, in 1958, Bruck’s colleague, J.M. Osborn, managed to show that diassociative, commutative A-loops are Moufang ([5]). In [2] we relaunched this now over 50 year old program by examining conditions under which...
On Multihomomorphisms
On multihomomorphisms.
On multiplication groups of left conjugacy closed loops
A loop is said to be left conjugacy closed (LCC) if the set is closed under conjugation. Let be such a loop, let and be the left and right multiplication groups of , respectively, and let be its inner mapping group. Then there exists a homomorphism determined by , and the orbits of coincide with the cosets of , the associator subloop of . All LCC loops of prime order are abelian groups.
On multiplication groups of relatively free quasigroups isotopic to Abelian groups
If is a quasigroup that is free in the class of all quasigroups which are isotopic to an Abelian group, then its multiplication group is a Frobenius group. Conversely, if is a Frobenius group, a quasigroup, then has to be isotopic to an Abelian group. If is, in addition, finite, then it must be a central quasigroup (a -quasigroup).
On multiplicative bases in abelian groups