In mathematics, subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group.[1]
Let be a finitely generated group. Then, for each integer define to be the number of subgroups of index in . Similarly, if is a topological group, denotes the number of open subgroups of index in . One similarly defines and to denote the number of maximal and normal subgroups of index , respectively.
Subgroup growth studies these functions, their interplay, and the characterization of group theoretical properties in terms of these functions.
The theory was motivated by the desire to enumerate finite groups of given order, and the analogy with Mikhail Gromov's notion of word growth.
^Alexander Lubotzky, Dan Segal (2003). Subgroup Growth. Birkhäuser. ISBN 3-7643-6989-2.
In mathematics, subgroupgrowth is a branch of group theory, dealing with quantitative questions about subgroups of a given group. Let G {\displaystyle...
theory of discrete groups and Kazhdan's property (T), the study of subgroupgrowth and applications of group theory to combinatorics and computer science...
subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple example is the subgroup of...
the genus Musa (bananas and plantains) placed in the African Plantain subgroup of the AAB chromosome group. Although "AAB" and "true plantain" are often...
of polynomial subgroupgrowth". Israel Journal of Mathematics. 82 (1–3): 363–371. doi:10.1007/BF02808118. —— (2000). "Closed Subgroups of Profinite Groups"...
finite group theory, particularly progress in the study of subgroupgrowth. Studying subgroups and lattices in linear groups, such as S L ( n , R ) {\displaystyle...
Serpentine subgroup (part of the kaolinite-serpentine group in the category of phyllosilicates) are greenish, brownish, or spotted minerals commonly found...
score of 679. Although it met the school-wide growth target, it did not meet the state subgroupgrowth targets. To encourage schools to improve achievement...
The Stability and Growth Pact (SGP) is an agreement, among all the 27 member states of the European Union, to facilitate and maintain the stability of...
1 has an exponential growth rate of order 2n − 1. A few other related results are: The Nielsen–Schreier theorem: Every subgroup of a free group is free...
Growth hormone therapy refers to the use of growth hormone (GH) as a prescription medication—it is one form of hormone therapy. Growth hormone is a peptide...
problems on fixed points of automorphisms of p-groups, and studied subgroupgrowth of profinite and discrete groups. From 1995 Shalev developed and applied...
groups, cultivars may be divided into subgroups and then given a cultivar name, e.g. Musa AAA Group (Cavendish Subgroup) 'Robusta'. In practice, the scoring...
rationality of a wide range of generating functions in group theory (e.g. subgroupgrowth) and number theory by various authors, notably Dan Segal and Marcus...
into several major groups: (1) The Ata subgroup: Dugbatang, Talaingod, and Tagauanum; (2) The Bagobo subgroup: Attaw (Jangan, Klata, Obo, Giangan, Guiangan)...
section 5.6. Lubotzky, Alexander; Segal, Dan (2003). "Chapter 7". Subgroupgrowth. Birkhäuser. Calegari, Danny (May 17, 2014). "A tale of two arithmetic...
Mary; Vishne, Uzi (2007), "Logarithmic growth of systole of arithmetic Riemann surfaces along congruence subgroups", Journal of Differential Geometry, 76...
year study period; in contrast, nearly 1 in 10 patients of the high risk subgroup progressed to TKR when treated with the placebo. These findings suggest...
Bakker in 1986 as a group including the relatively derived theropod subgroups Ceratosauria and Tetanurae, and excluding coelophysoids. However, most...
group which behaves like a subgroup "up to a constant error", in a precise quantitative sense (so the term approximate subgroup may be more correct). For...
B Cell Growth and Differentiation Factors (also known as BCGF and BCDF) are two important groups of soluble factors controlling the life cycle of B cells...
senior military officials. In October 2023, it was reported that there was a growth of mutinies among Russian troops due to large amount of losses in Russian...
vast geographical expanse, the Han Chinese can be divided into various subgroups based on their respective cultural, ethnic, genetic, linguistic, and regional...
Global Information
