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.
Step by Step Answer:
True a Every group has a presentation True b Every group has many diffe...View the full answer
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