TY - JOUR
T1 - Graphs, partitions and classes of groups
AU - Ballester-Bolinches, Adolfo
AU - Cossey, John
PY - 2012/6
Y1 - 2012/6
N2 - If X is a class of groups, Delizia et al. (Bull Austral Math Soc 75:313-320, 2007) call a group G X -transitive (or an XT -group) if whenever 〈 a, b 〉 and 〈 b, c〉 are in X 〈a, c〉 is also in X (a, b, c ∈ G). The structure of XT-groups has been investigated for a number of classes of groups, by Delizia, Moravec and Nicotera and others. A graph can be associated with a group in many ways. Delizia, Moravec and Nicotera introduce a graph which is a generalisation of the commuting graph of a group, but do not make use of the graph. We will use the properties of the graph to investigate further classes of groups and to obtain more detailed structural information.
AB - If X is a class of groups, Delizia et al. (Bull Austral Math Soc 75:313-320, 2007) call a group G X -transitive (or an XT -group) if whenever 〈 a, b 〉 and 〈 b, c〉 are in X 〈a, c〉 is also in X (a, b, c ∈ G). The structure of XT-groups has been investigated for a number of classes of groups, by Delizia, Moravec and Nicotera and others. A graph can be associated with a group in many ways. Delizia, Moravec and Nicotera introduce a graph which is a generalisation of the commuting graph of a group, but do not make use of the graph. We will use the properties of the graph to investigate further classes of groups and to obtain more detailed structural information.
KW - Classes of groups
KW - Finite groups
KW - Graphs
KW - Partitions
KW - Permutability
UR - http://www.scopus.com/inward/record.url?scp=84861625740&partnerID=8YFLogxK
U2 - 10.1007/s00605-010-0263-3
DO - 10.1007/s00605-010-0263-3
M3 - Article
SN - 0026-9255
VL - 166
SP - 309
EP - 318
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
IS - 3-4
ER -