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Simple infinite groups Infinite group for which it is still unknown if it is simple

Is there an example aboutof an infinite group for which isit is still unknown ifwhether or not it is simple or not?. On the other hand, 

Is there a criterion for determining the simplicity of infinite groups?

Simple infinite groups

Is there an example about an infinite group which is still unknown if it is simple or not?. On the other hand, Is there a criterion for determining the simplicity of infinite groups?

Infinite group for which it is still unknown if it is simple

Is there an example of an infinite group for which it is still unknown whether or not it is simple? 

Is there a criterion for determining the simplicity of infinite groups?

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Simple infinite groups

Is there an example about an infinite group which is still unknown if it is simple or not?. On the other hand, Is there a criterion for determining the simplicity of infinite groups?