@article {
author = {Brough, Julian},
title = {The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups},
journal = {International Journal of Group Theory},
volume = {8},
number = {4},
pages = {1-3},
year = {2019},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2018.110074.1472},
abstract = {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.},
keywords = {Conjugacy classes,finite groups,restriction to substructures},
url = {http://ijgt.ui.ac.ir/article_23001.html},
eprint = {http://ijgt.ui.ac.ir/article_23001_d14fcde9b40ecb50266a73a05dc9479a.pdf}
}