SE-supplemented subgroups of finite groups
Several quantitative characterizations of some specific groups
Let be a finite group and let be the set of prime divisors of for which . The Gruenberg-Kegel graph of , denoted , is defined as follows: its vertex set is and two different vertices and are adjacent by an edge if and only if contains an element of order . The degree of a vertex in is denoted by and the -tuple is said to be the degree pattern of . Moreover, if is the vertex set of a connected component of , then the largest -number which divides , is said to be an...
Sharply 2- and 3-transitive groups with kernels of finite index.
Simple group contain minimal simple groups.
It is a consequence of the classification of finite simple groups that every non-abelian simple group contains a subgroup which is a minimal simple group.
Simple groups in computational group theory.
Simple groups of square order and interesting sequence of primes
Simple groups, permutation groups, and probability.
Simply connected coset complexes for rank 1 groups of Lie type.
Simulated factorizations II.
SK... for finite group rings: II.
SK1 of finite group rings: V.
Small maximal sum-free sets.
Small-sum pairs in abelian groups
Let be an abelian group and two subsets of equal size such that and both have size . Answering a question of Bihani and Jin, we prove that if is aperiodic or if there exist elements and such that has a unique expression as an element of and has a unique expression as an element of , then is a translate of . We also give an explicit description of the various counterexamples which arise when neither condition holds.
Smith equivalence and finite Oliver groups with Laitinen number 0 or 1.
Solitary quotients of finite groups
We introduce and study the lattice of normal subgroups of a group G that determine solitary quotients. It is closely connected to the well-known lattice of solitary subgroups of G, see [Kaplan G., Levy D., Solitary subgroups, Comm. Algebra, 2009, 37(6), 1873–1883]. A precise description of this lattice is given for some particular classes of finite groups.
Solubility of Finite Groups Admitting a Fixed-Point-Free Automorphism of Order rst. IV.
Solubility of Groups Admitting a Fixed-point-free Automorphism Group of Type (p, p).
Solubility of Groups Admitting Certain Fixed-Point-Free Automorphism Groups.
Soluble products of connected subgroups.
Solvable finite groups with a particular configuration of Fitting sets
A Fitting set is called elementary if it consists of the subnormal subgroups of the conjugates of a given subgroup. In this paper we analyse the structure of the finite solvable groups in which every Fitting set is the insiemistic union of elementary Fitting sets whose intersection is the subgroup 1.