Element prime order (EPO) group

Question

A finite group $G$ is called EPO-group if every non-identity element of $G$ has prime order.

For a given finite group $G$, let $\pi (G)$ denote the set of all prime divisors of $|G|$.

Does there exist non-isomorphic EPO-groups $G_1$, $G_2$ of same order with $|\pi(G_i)|\geq 2$ , $i=1,2$ ?

verret · Accepted Answer · 2017-01-18T17:10:42.023

4

The smallest examples are the groups denoted (147,4) and (147,5) in the SmallGroups library. They are both semidirect products $Z_7^2:Z_3$.

edited Jan 18 '17 at 17:10

answered Jan 17 '17 at 21:27

verret

score 3 · Answer 2 · edited Apr 13 '17 at 12:19

3

Yes, finite, non-isomorphic EPO-groups of the same order are possible. See DonAntonio's answer to a question in the recent thread

edited Apr 13 '17 at 12:19

Community

answered Jan 17 '17 at 14:51

quasi

Thank you quasi for pointing out this post, but actually I want to know some thing more, which I have now explained in this edited post. – RKR Jan 17 '17 at 15:22

2 Answers2