Hungarian Historical Phonology ágyék
ágyék 'loins'
First attestation/Old Hungarian data
[coming]
Important dialectal forms
ágyíka 'a csizmatalp hajlása' (Sarkad; ÚMTSz I: 168, s.v. ágyék)
Uralic/Ugric/Pre-Hungarian reconstruction
*ońća 'meat, share'
Aikio 2015: 61: *onśa 'meat, share'
UEW: PUg *ańćɜ 'hair; Haar'
Zhivlov 2014: 143: PU *a/ońća1 'back'
Status of the Ugric etymology
Plausible, but probably derived from PU (see below)
Loan etymology
PU ← IIr *(H)anća- (Koivulehto 2001; Holopainen 2019)
Cognates suggested in earlier research
UEW:
Mansi: South (TJ) ońćī 'das Hintere', East (KU) uńś 'das Hintere', West (P) wuńś 'das Hintere', North (N) ūńś 'segg; Arsch' < PMs *ūńć
Sammallahti 1988: 542:
Mansi: South (TJ) ońćī 'das Hintere', East (KU) uńś 'das Hintere', West (P) wuńś 'das Hintere', North (N) ūńś 'segg; Arsch' < PMs *ūńć
Finnish: osa 'part'
Saami: N oažži 'flesh'
Aikio 2015: 61:
Mansi: South (TJ) ońćī 'das Hintere', East (KU) uńś 'das Hintere', West (P) wuńś 'das Hintere', North (N) ūńś 'segg; Arsch' < PMs *ūńć
Finnish: osa 'part'
Saami: N oažži 'flesh'
Mari: užaš 'part, share'
Commentary
The Ugric etymology presented in the UEW is regular, but the Hungarian and Mansi words have been connected to Finnish osa and Saami oažži already by Sammallahti (1988). Aikio (2015) adds Mari užaš here. Phonologically the Uralic etymology is regular, but the semantic differences are rather big. Zhivlov (2014) reconstructs PU *a/ońća1 'back' as a source of Hungarian ágyék and Mansi *ūńć.
If we accept a semantic change 'meat' > 'bottocks', the Uralic etymology for the Hungarian and Mansi words can be accepted. In this case it is possible that Hungarian and Mansi reflect a common semantic innovation.
A Proto-Indo-Iranian etymology for PU *ońća has been suggested by Koivulehto (2001).
Conclusion
The Proto-Uralic etymology is convincing. The meaning 'hair' in Hungarian and Mansi might reflect a common semantic innovation.
References
Aikio 2013: 166–167: PU
Aikio 2015: 52: PU
UEW s.v. kajɜ: Proto-Ugric Uralonet
Zhivlov 2014: 143: PUg/PU