Why does the second and third person singular and second person plural of bekommen not follow the convention of adding an -e- before the personal endings in the Simple Present tense?
Does it have to do with indicative vs. subjunctive mood?
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The rule that is given in Schaum's Outline for the simple present tense (indicative) is written in a somewhat confusing way. It should be read
When an infinitive stem ends in -m or -n preceded by a consonant other than "l", "r", "m", "n", or "h", or if it ends in -d or -t, then -e- is added.
That means, the rule does not apply to verbs like kommen, leimen, qualmen, wärmen, lahmen, because the additional consonant is missing. The fact that kommen is a strong verb is not relevant here; the weak verb kämmen behaves in the same way.
In fact, I can only think of one common verb with an infinitive stem ending in -m where the rule does apply, namely atmen. For -n, there are more.
In the subjunctive present, the endings are always -e, -est, -e, -en, -et, -en (except for "sein"). They do not depend on the final consonant of the stem.
Regular verbs with a stem ending with -m (also with t; d; or n) add an extra e for the 2nd. and 3rd. person singular and 2nd. person plural.
The following verbs belong in that group:
antworten; arbeiten; atmen; begegnen; beobachten; bilden; bitten; finden; gründen; heiraten; mieten; öffnen; rechnen; reden; retten; trocknen; warten; zeichnen
The verbs with endings -lm; -ln and -rn are exceptions to this rule: e.g. lernen and qualmen
Why should there be an extra 'e'?
An 'e' is inserted in e.g., reden (er/sie/es redet, ihr redet) because you cannot pronounce "redt" well.
In old forms of German (or when people want to impress you on the Mittelaltermarkt) you may find an 'e' where nowadays none is inserted: 'saget doch' vs 'sagt doch', 'nehmet' vs 'nehmt'.