The Number of Conjugacy Classes of Nonnormal Cyclic Subgroups in Nilpotent Groups
Received:June 28, 2004  
Key Words: nilpotent group   nonnormal subgroup   number of conjugacy classes  
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Author NameAffiliation
ZHONG Xiang-gui School of Math. \& Comput. Sci., Guangxi Normal University, Guilin 541004, China 
LI Shi-rong School of Math. \& Info. Sci., Guangxi University, Nanning 530004, China 
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Abstract:
      This paper proves that for a nilpotent group $G$ of nilpotency class $c=c(G),$ the number $v^*(G)$ of conjugacy classes of nonnormal cyclic subgroups satisfies the inequality $v^*(G)\geq c(G)-1,$ or $G$ is a Hamiltonian group, or there is a normal subgroup $K$ of $G$ such that $K/Z(K)$ has a homomorphic image isomorphic to the dihedral group $D(2^n)$ with $n\geq 3$ or $C_2\times C_2.$
Citation:
DOI:10.3770/j.issn:1000-341X.2006.03.020
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