Mark each of the following true or false. ___ a. Every group has a presentation. ___ b.

Question:

Mark each of the following true or false. 

___ a. Every group has a presentation. 

___ b. Every group has many different presentations. 

___ c. Every group has two presentations that are not isomorphic. 

___ d. Every group has a finite presentation. 

___ e. Every group with a finite presentation is of finite order. 

___ f. Every cyclic group has a presentation with just one generator. 

___ g. Every conjugate of a relator is a consequence of the relator. 

___ h. Two presentations with the same number of generators are always isomorphic. 

___ i. In a presentation of an abelian group, the set of consequences of the relators contains the commutator subgroup of the free group on the generators. 

___ j. Every presentation of a free group has 1 as the only relator.

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