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My primary source for my Black Sea Campaign are the German General Staff of the Army situation maps. They were compiled every day in the evening.
For example, the map from the evening of 13th August 1941 shows LSSAH northeast of Nikolaev.
As i read it, it shows that parts of the division had to stay back and fight around Novyi Buh, while most of the division was moving southwards next to the 16th Panzer-Division while the 16th was closing the pocket. Meanhwile the 3 hungarian brigades (two motorized, one cavalry) appoached Nikolaev from the north.
The recon detachement of LSSAH is furthest to the south(east) of the LSSAH division.
Unfortunately the area of interest is not part of my Nikolaev map (no. 1502). Its the eastern map edge at best.
A.A.= Aufklärungsabteilung, recon detachement
Tle. = Teile, parts (of a division)
Fähre = ferry
st. mot. Einzel-Verk = heavy motorized single traffic. Probably means unorganized retreat of dispersed units?
zerl. Kol. all. Waffen = dismantled columns of all kind of weapons. Retreating enemy. I am not sure if that "dismantled" means the artillery etc. is in transport condition or the columns were "dismantled", meaning dispersed?
V.A. Vorausabteilung = a vanguard of combined motorized arms. For example, a recon detachment, a coy infantry, a coy engineers, a battery of artillery and a AT platoon. All motorized. But could be mixed ad hoc formatios as well i guess.
9 Zge. = 9 Züge, 9 trains
ung. Schn. Kps. = ungarisches schnelles Korps, Hungarian Rapid Corps, "Gyorshadtest".
The only other map about the battle of Nikolaev i found, is this one: