A Characterization of Groups (Solved)

Summary: Suppose the semigroup S contains an element g such that (i) for each x in S there is some y in S such that gy = x, and (ii) for each x in S there is some y in S such that yx = g. Show that S is a group.

Classification: Primary, Algebra; Secondary, Abstract Algebra

Torben Maack Bisgaard
Nandrupsvej 7 st. th.
DK-2000 Frederiksberg C
Denmark
e-mail: torben.bisgaard@get2net.dk
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