Finite groups with conjugacy classes number one greater than its same order classes number

Details Finite groups with conjugacy classes number one greater than its same order classes number Finite groups with conjugacy classes number one greater than its same order classes number

2005-09-16

arxiv.org/abs/math/0509376v1

Mathematics

Group Theory

15 pages

Scientific paper

Let $k(G)$ be the number of conjugacy classes of finite groups $G$ and $\pi_e(G)$ be the set of the orders of elements in $G$. Then there exists a non-negative integer $k$ such that $k(G)=|\pi_e(G)|+k$. We call such groups to be $co(k)$ groups. This paper classifies all finite $co(1)$ groups. They are isomorphic to one of the following groups: $A_5, L_2(7), S_5, Z_3, Z_4, S_4, A_4$, $D_{10}, Hol(Z_5)$, or $Z_3\rtimes Z_4$.

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