we call $h$ an $ss$-embedded subgroup of $g$ if there exists a‎ ‎normal subgroup $t$ of $g$ such that $ht$ is subnormal in $g$ and‎ ‎$hcap tleq h_{sg}$‎, ‎where $h_{sg}$ is the maximal $s$-permutable‎ ‎subgroup of $g$ contained in $h$‎. ‎in this paper‎, ‎we investigate the‎ ‎influence of some $ss$-embedded subgroups on the structure of a‎ ‎finite group $g$‎. ‎some new results were obtained.‎

In an earlier paper [S] we have determined the structure of the linear groups over a local ring. In this note we continue the study of the classical groups over a local ring with the investigation of the orthogonal groups. Our main result (cf. Theorem 6 below) is a complete description of the invariant subgroups of an orthogonal group of noncompact type (i.e., of index ^ 1) over a local ring L ...

The results of the analysis of the subclustering in a sample of ESO Nearby Abell Cluster Survey (ENACS) galaxy clusters, with data complemented from other studies, are presented. The analysis is performed by using the S-tree method enabling one to study the hierarchical properties of clusters, namely by the detection of the main physical cluster and of its subgroups. The results indicate: (a) s...

• Finite Groups: The maximal subgroup machinery is now able to access the maximal subgroups and automorphism groups of a greatly expanded set of simple groups. These include HS and L(6, 2), Alt(d) (d < 1000), L(2, p), L(2, p), L(2, p), L(3, p), L(3, 8), L(3, 9), S(4, p), and U(3, p) (p prime). This greatly extends the range of those algorithms used for determining subgroups and automorphism gro...

The graph-theoretical S-tree technique developed for the study of the nonlinear Nbody systems, is used for the study for the first time of the substructure of a high redshift cluster of galaxies, namely of MS 1054-03, z ≃ 0.8. Nearby galaxy clusters studied via the same S-tree code reveal several clearly distinguished subgroups with significant bulk velocities. Therefore the study of distant cl...

OBJECTIVE To examine test-retest reliability and internal consistency of the Children's Social Desirability Short (CSD-S) scale, consisting of 14 items from the Children's Social Desirability scale. METHODS The previously validated CSD-S scale was classroom administered to 97 fourth-grade children (80% African American; 76% low socioeconomic status) in 2 sessions a month apart. Each classroom...

We show that given a collection $$X=\{f_1$$ , ..., $$f_m\}$$ of pure mapping classes on surface S, there is an explicit constant N, depending only X, such their Nth powers $$\{f_1^N$$ $$f_m^N\}$$ generate the expected right-angled Artin subgroup MCG(S). Moreover, we these subgroups are undistorted, and each element pseudo-Anosov largest possible subsurface.