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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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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