Group Theory

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Across
  1. 2. a subset of G that forms group under the same operation
  2. 5. The group which is commutative
  3. 6. Non cyclic group of order four
  4. 8. For each element a in the group there exist an element b such that a.b=e=b.a
  5. 10. The group of all permutations on a finite set
Down
  1. 1. Two groups are isomorphic if there exists a bijective homomorphism between them
  2. 3. A group generated by a single element
  3. 4. The theorem in which the order of any subgroup divides the order of the group
  4. 7. There exists an element e in group such that e.a = a = a.e
  5. 9. A subgroup that is invariant under conjugation, meaning gHg^(-1) = H