TY - JOUR
T1 - On Non-Commuting Sets in a Finite $p$-Group with Derived Subgroup of Prime Order
AU - Wang , Yulei
AU - Liu , Heguo
JO - Communications in Mathematical Research 
VL - 3
SP - 193
EP - 197
PY - 2021
DA - 2021/05
SN - 32
DO - http://doi.org/10.13447/j.1674-5647.2016.03.01
UR - https://global-sci.org/intro/article_detail/cmr/18891.html
KW - finite $p$-group, non-commuting set, cardinality.
AB - <p style="text-align: justify;">Let $G$ be a finite group. A nonempty subset $X$ of $G$ is said to be non-commuting if $xy≠yx$ for any $x, y ∈ X$ with $x≠y$. If $|X| ≥ |Y|$ for any other
non-commuting set $Y$ in $G$, then $X$ is said to be a maximal non-commuting set. In
this paper, we determine upper and lower bounds on the cardinality of a maximal
non-commuting set in a finite $p$-group with derived subgroup of prime order.</p>