subnormal subgroup
21Lattice of subgroups — In mathematics, the lattice of subgroups of a group G is the lattice whose elements are the subgroups of G, with the partial order relation being set inclusion.In this lattice, the join of two subgroups is the subgroup generated by their union,… …
22Fitting length — In mathematics, especially in the area of algebra known as group theory, the Fitting length (or nilpotent length) measures how far a solvable group is from being nilpotent. The concept is named after Hans Fitting, due to his investigations of… …
23Quasisimple group — In mathematics, a quasisimple group (also known as a covering group) is a group that is a perfect central extension E of a simple group S . In other words, there is a short exact sequence:1 rarr; Z ( E ) rarr; E rarr; S rarr; 1such that E = [ E …
24Solvable group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …
25Chief series — In abstract algebra, a chief series is a maximal normal series for a group. It is similar to a composition series, though the two concepts are distinct in general: a chief series is a maximal normal series, while a composition series is a maximal …
26Polycyclic group — In mathematics, especially in the area of abstract algebra known as group theory, a polycyclic group is a solvable group that satisfies the maximal condition on subgroups (that is, every subgroup is finitely generated).Equivalently, a group G is… …
27Herzog–Schönheim conjecture — In mathematics, the Herzog–Schönheim conjecture is a combinatorial problem in the area of group theory.Let G be a group, and let:A={a 1G 1, ldots, a kG k}be a finite system of left cosets of subgroupsG 1,ldots,G k of G.In 1974 M. Herzog and J.… …
28Iwasawa group — In mathematics a group is sometimes called an Iwasawa group or M group or modular group if its lattice of subgroups is modular.Finite modular groups are also called Iwasawa groups, after harv|Iwasawa|1941 where they were classified. Both finite… …
29Life Sciences — ▪ 2009 Introduction Zoology In 2008 several zoological studies provided new insights into how species life history traits (such as the timing of reproduction or the length of life of adult individuals) are derived in part as responses to… …
