Is it permissible for a man to pray while wearing a singlet?
Praying while wearing a singlet or other type of clothing which exposes the shoulders or shirtless is makruh but his prayer is still valid. Rasullullah PBUH said:
لاَ يُصَلِّي أَحَدُكُمْ فِي الثَّوْبِ الْوَاحِدِ لَيْسَ عَلَى عَاتِقَيْهِ مِنْهُ شَىْءٌ
“None of you should offer Salat (prayer) in a single garment with no part of it on his shoulders.” 
According to Imam al-Nawawi, “The wisdom for this is that if he wears certain clothing and nothing is covering his shoulders, then it isn’t safe for his awrah from getting uncovered, it is different if he places a type of clothing on his shoulders. Imam Malik, Imam Abu Hanifah, Imam Al-Syafie and the jumhur of scholars hold the opinion: The restriction showed the makruh tanzih ruling and not its prohibition. If a person prays while just wearing a type of clothing which covers his awrah, however, it doesn’t cover his shoulders, then his prayer is valid but makruh, regardless of whether he can place something on his shoulders or otherwise.” 
Although his prayer is valid, it is best to wear appropriate and neat clothing while one is praying. Let’s reflect on the following statement of Allah SWT:
يَا بَنِي آدَمَ خُذُوا زِينَتَكُمْ عِندَ كُلِّ مَسْجِدٍ
“O children of Adam, take your adornment at every masjid,” 
Imam al-Tabari rahimahullah in his commentary stated the word خُذُوا زِينَة in the verse means clothing that covers the awrah. We supplicate to Allah SWT so that we’ll be given the correct understanding in practising our religion. Wallahua’lam.
 Narrated by Al-Bukhari, no. 359; Riwayat Muslim, no. 516.
 Sharḥ al-Nawawī ʿalā Muslim, 2/274