Treffer: Groups with few class sizes and the centraliser equality subgroup: Groups with few class sizes and the centraliser equality subgroup.
Title:
Groups with few class sizes and the centraliser equality subgroup: Groups with few class sizes and the centraliser equality subgroup.
Authors:
Source:
Israel Journal of Mathematics. 142:367-380
Publisher Information:
Springer Science and Business Media LLC, 2004.
Publication Year:
2004
Subject Terms:
characteristic subgroups, metabelian \(p\)-groups, 4. Education, upper central series, Subgroup theorems, subgroup growth, 0102 computer and information sciences, 01 natural sciences, normal subgroups, finite \(p\)-groups, Special subgroups (Frattini, Fitting, etc.), Finite nilpotent groups, \(p\)-groups, centralizers, breadths, 0101 mathematics, conjugacy class sizes, Arithmetic and combinatorial problems involving abstract finite groups, Conjugacy classes for groups
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
Language:
English
ISSN:
1565-8511
0021-2172
0021-2172
DOI:
10.1007/bf02771541
Access URL:
Rights:
Springer TDM
Accession Number:
edsair.doi.dedup.....e313779e1d69aec45a95af6df2709cf8
Database:
OpenAIRE
Weitere Informationen
Let \(G\) be a finite \(p\)-group and let \(G\) have conjugacy class sizes \(1=n_12\), then \(\exp(G/D(G))\leq 2^{k-2}\). We have \(D(G)\geq Z(G)\). If \(\exp(G)=p\), then \(D(G)=Z(G)\). If \(G\) is a \(2\)-group of maximal class and order \(>2^3\), then \(D(G)\) is a cyclic subgroup of index \(2\) in \(G\). If \(D(G)\leq H\leq G\) and \(\text{cl}(H)\leq p\), then \(D(G)\leq Z(H)\). Next, \(C_G(D(G))\geq Z_p(G)\), the \(p\)-th member of the upper central series of \(G\). The subgroup \(C_G(D)\) contains all normal subgroups of \(G\) of class \(