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Tuesday, 22 January 2013

The ABC theorem

Theorem Let A,B,C be subgroups of G. Let BAG and CG, then we have:
A) ABC=B(AC) as sets.
B) if BA then BCAC and (AC)/(BC)B(AC)/B
C) If BA and CG then BCAC and AC/BCA/B(AC).
proof hint: Use Noethers isomorphism theorems and sometimes consider elements.

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