Green’s Dictionary of Slang

armpit n.

[the link of the SE armpit with dirt and smell]

1. (orig. US) the least appetizing, poorest, most run-down and poss. dangerous area of a city or town; often as armpit of the nation/universe; also in phr. rough as a docker’s armpit.

2. (orig. US) used similarly of a place, e.g. a nightclub or café.

3. (US campus) an unpleasant individual.

In phrases

put someone up to their armpits (v.)

[mid-19C] (UK Und.) to cheat an accomplice out of his share of the proceeds.

SE in slang uses

In phrases

up to one’s armpits (also up to one’s diddies,’s nipples,’s tits, over one’s tits) [var. on up to the elbows under elbow n.1 ]

[19C+] (orig. US) consumed by, overwhelmed by.

work under the armpits (v.) [SE work/work v. (4); ? above the armpits is the neck from which one can be hanged, so below this fig. line one is ‘safe’]

[early 19C] (UK Und.) to confine one’s criminality to such activities that would be classed as petty larceny, bringing a maximum sentence of seven years transportation, rather than hanging; thus work above the armpits v., to commit crimes that could lead to one’s execution.