Brief sketch on wiki here fyi: https://en.wikipedia.org/wiki/Slovak_Expeditionary_Army_Group

The single reference is to the Slovakia chapter in 'Joining Hitler's Crusade: European Nations and the Invasion of the Soviet Union, 1941' by Jan Rychlík. I tracked down the doi number, unlocked on sci-hub here if you fancy a concise 27 page read on the role of Slovakia in WW2 (army section starts from p.12): https://sci-hub.yncjkj.com/10.1017/9781108225281.006

Briefly, it looks like the Slovak division involved in the German advance went south in the attempt to occupy the oil fields in the Caucasus - Group B (Group A went for Stalingrad). A lot of the named towns sound familiar: Vinnitsia, Kiev, Lvov, Kharkov, Rostov. They were caught by the Russian counter-offensive in Melitopol where lots of them refused to fight and were taken prisoner (morale undermined by the cold winter and partly not wanting to fight for the Germans any more). A 'security' division stayed in northern Ukraine where they were supposed to do a 'cleanup' operation against partisans. Some punitive massacres but other instances of defections and collaboration with pro-soviet forces, the author says they didn't have much involvement with the UPA 'nationalists'. Some anti-Jewish abuses, thefts and murders, and the right wing government of the supposedly independent Slovak government (in fact dominated by Germany) collaborated with the final solution.

Interesting history, thanks T for the prompt to look into it.

I