For a finite group G, subgroup P of G is 2-minimal if B<P, where B=NG(S) for some Sylow 2-subgroup S and B contained in unique maximal P. fields odd characteristic, this paper contains detailed explicit description all the subgroups general orthogonal groups, certain their subgroups.

Numerical analysis of Saxifraga in Iran was carried out on the basis of morphological and chorological data. The cluster analysis confirmed that the genus in Iran includes two distinct groups: Group one consists of two subgroups, a) alpine Irano-Turanian endemic species (S. ramsarica, S. iranica, S. wendelboi, S. koelzii), and b) Euxino-Hyrcanian species (S. paniculata subsp. Cartilaginea, S. k...

let $mathfrak{f}$ be a formation and $g$ a finite group. a subgroup $h$ of $g$ is said to be weakly $mathfrak{f}_{s}$-quasinormal in $g$ if $g$ has an $s$-quasinormal subgroup $t$ such that $ht$ is $s$-quasinormal in $g$ and $(hcap t)h_{g}/h_{g}leq z_{mathfrak{f}}(g/h_{g})$, where $z_{mathfrak{f}}(g/h_{g})$ denotes the $mathfrak{f}$-hypercenter of $g/h_{g}$. in this paper, we study the structur...

This paper and its sequel [17] deal with a range of questions about the subgroup structure of infinite symmetric groups. Our concern is with such questions as the following. How can an infinite symmetric group be expressed as the union of a chain of proper subgroups? What are the subgroups that supplement the normal subgroups of an infinite symmetric group? What are the maximal proper subgroups...