TY - JOUR
ID - 23001
TI - The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Brough, Julian
AD - Fachgruppe Mathematik und Informatik, BU Wuppertal, Wuppertal, Germany
Y1 - 2019
PY - 2019
VL - 8
IS - 4
SP - 1
EP - 3
KW - Conjugacy classes
KW - finite groups
KW - restriction to substructures
DO - 10.22108/ijgt.2018.110074.1472
N2 - We say that a group $G$ satisfies the one-prime power hypothesis for conjugacy classes if the greatest common divisor for all pairs of distinct conjugacy class sizes are prime powers. Insoluble groups which satisfy the one-prime power hypothesis have been classified. However it has remained an open question whether the one-prime power hypothesis is inherited by normal subgroups and quotients groups. In this note we construct examples to show the one-prime power hypothesis is not necessarily inherited by normal subgroups or quotient groups.
UR - http://ijgt.ui.ac.ir/article_23001.html
L1 - http://ijgt.ui.ac.ir/article_23001_d14fcde9b40ecb50266a73a05dc9479a.pdf
ER -