The Journal of the Indian Mathematical Society

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Notes on Group-Theory IV-VI


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1 Calcutta, India
     

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This note deals with groups which are formed by two groups, say A and B, using certain homomorphisms. The resulting group [A, B] will be shown to be commutative and to depend on A/C(A) and B/C(B) only. When the two factorgroups admit representation by finite bases^ a similar representation of [A, B] can be derived (§3). Some results can be generalized for arbitrary groups A and B. Applications of the groups [A, B] will be made in some of the subsequent notes.
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  • Notes on Group-Theory IV-VI

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Authors

F. W. Levi
Calcutta, India

Abstract


This note deals with groups which are formed by two groups, say A and B, using certain homomorphisms. The resulting group [A, B] will be shown to be commutative and to depend on A/C(A) and B/C(B) only. When the two factorgroups admit representation by finite bases^ a similar representation of [A, B] can be derived (§3). Some results can be generalized for arbitrary groups A and B. Applications of the groups [A, B] will be made in some of the subsequent notes.