Thank you. That was very helpful, Istvan.

That's not really the case. It is actually not conjugated in the indefinite. It is a (perhaps unique) feature of the Hungarian language that the object can often be omitted after the verb. However, "Ö nem ismer" translates both to "He doesn't know me" or He doesn't know you". This depends on the context. Let's take another example: They don't know him. (Ők) nem ismerik (őt). As you can see, I put the words which can be omitted in brackets. However, it is not really a mistake if you don't omit these. There is also indefinite conjugation of verbs in Hungarian, but I wouldn't go into details about that now.

I figured it out. Me is the object, but it's 1st person, so it's conjugated in the indefinite.