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Longman Dictionary of Contemporary English
air commodore
noun
EXAMPLES FROM CORPUS
▪ The following month he received a permanent commission in the Royal Air Force, soon afterwards being promoted air commodore.
Wiktionary
air commodore

n. (alternative case form of air commodore nodot=1 English) (qualifier: found when the term is used as a title).

Wikipedia
Air commodore

Air commodore (abbreviated as Air Cdre in the RAF, IAF and PAF; AIRCDRE in the RNZAF and RAAF) is a one-star rank and the most junior general rank of the air-officer which originated in and continues to be used by the Royal Air Force. The rank is also used by the air forces of many countries which have historical British influence such as Bangladesh, and it is sometimes used as the English translation of an equivalent rank in countries which have a non-English air force-specific rank structure. The name of the rank is always the full phrase and is never shortened to Commodore, which is a rank in various naval forces.

Air commodore is a one-star rank and the most junior air officer rank, being immediately senior to group captain and immediately subordinate to air vice-marshal. It has a NATO ranking code of OF-6 and is equivalent to a commodore in the Royal Navy or a brigadier in the British Army or the Royal Marines. Unlike these two ranks, however, it has always been a substantive rank. Additionally, air commodores have always been considered to be air officers whilst Royal Navy commodores have not since the Napoleonic Wars been classified as officers of flag rank, and British Army brigadiers have not been considered to be general officers since 1922 when they ceased to be titled as brigadier-generals. In other NATO forces, such as the United States Armed Forces and the Canadian Armed Forces, the equivalent one-star rank is brigadier general.

The equivalent rank in the Women's Auxiliary Air Force, Women's Royal Air Force (until 1968) and Princess Mary's Royal Air Force Nursing Service (until 1980) was "air commandant".

Usage examples of "air commodore".

The hurrying figure of the air commodore was already almost lost to sight.

There was to be a cocktail party and dinner to honour the arrival of his British counterpart, Air Commodore Rodman, for the formal signing of the joint Bases Agreement at Celle and Fassberg.

Whenever that came, Air Commodore Teeghe said, he'd be grateful if they got right on it.

A brigadier, an air commodore, two men in overalls and a frightened-looking Wren with her fingers in her ears were standing round the edge of the room staring at a large machine full of revolving drums.