Roman Jakobson tells us that ‘Mayakovskij and I worked on his Soviet Alphabet together.When he had the first line of a couplet, but the second wouldn’t come to him, he would say: “I’ll pay you so much, if you can think up a good one!” There are quite a few of our joint verses there.’
It amused him a lot. There existed a school-boys’ pastime — indecent aphabets, and several of these verses recall them somewhat. Some of these alphabets existed in manuscript form and even were sold underground. The association was obvious and for this reason Mayakovskij was attacked terribly for his Alphabet.
— Roman Jakobson, My Futurist Years, New York: Marsilio Publishers, 1997, pp.50-51.
A Soviet Alphabet was written in the second half of September, 1919 and appeared in October that year. Mayakovsky’s recollections:
It was written as a parody on an old pornographic alphabet… It was written for use by the army. There were witticisms there that weren’t fit for salons, but which went quite well in the trenches…After writing the book I took it to the Central Printing House to have it typed. There was a typist there who hadn’t yet been purged, who told me with great malice: ‘Better I should lose my job than type this filth.’ So it started. Further on, no one wanted to print the book. … I had to publish it myself… I made three to five thousand copies by hand and carried the whole weight on my back to distribute it. This was genuine work by hand at the time of the most ominous encirclement of the Soviet Union.
— A speech at the House of the Komsomol on 25 March, 1930, quoted in Roman Jakobson, My Futurist Years, New York: Marsilio Publishers, 1997, pp.289-290.
Apparently there was a theatrical version too:
— From Joel Shcechter, Popular Theatre: a Sourcebook.