I desire (βουλομα). So Philippians 1:12.

The men (τους ανδρας). Accusative of general reference with the infinitive προσευχεσθα. The men in contrast to "women" (γυναικας) in 1 Timothy 2:9. It is public worship, of course, and "in every place" (εν παντ τοπω) for public worship. Many modern Christians feel that there were special conditions in Ephesus as in Corinth which called for strict regulations on the women that do not always apply now.

Lifting up holy hands (επαιροντας οσιους χειρας). Standing to pray. Note also οσιους used as feminine (so in Plato) with χειρας instead of οσιας. The point here is that only men should lead in public prayer who can lift up "clean hands" (morally and spiritually clean). See Luke 24:50. Adverb οσιως in 1 Thessalonians 2:10 and οσιοτης in Ephesians 4:24.

Without wrath and disputing (χωρις οργης κα διαλογισμου). See Philippians 2:14.