It is "оперативный сотрудник" or "оперативник". Agent is correct, Operating officer is also correct:)

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As previously discussed here and elsewhere, this may mean a variety of things. I am guessing that the опер here is an участковый (уполномоченный), that is a militia officer attached to the given district. This is the practice that survived to present day Russia. Translated into today's US speak, this is a neighborhood cop who regularly walks the beat, knows the area and has no trouble identifying newcomers. If this does not fit the context, you can choose from the what the others have offered.

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I would suggest transliterating it as it is - "oper" - as you did it with kulaks, and giving a translator's remark as to this Soviet archaism which has nothing in common with today's Russian police "опер". In Russian we have "копы" for "cops" in the same manner. Trying to find an English equivalent will kill the taste of scornful Russian contraction for "оперуполномоченный сотрудник".

Below are a few quotations from Solzhenitsyn - please check them out.

Но, давно в штабном бараке обжившись, он доступ имел в кабинеты майора, и начальника режима, и кума <Кум — по-лагерному — оперуполномоченный, — прим. автора>, услуживал им, порой слышал такое, чего не знали и надзиратели, и с некоторых пор посчитал, что мыть полы для простых надзирателей ему приходится как бы низко. <…>
И сразу шу-шу-шу по бригаде: Пантелеев, сука, опять в зоне остался. Ничего он не болен, опер его оставил. Опять будет стучать на кого-то. <…>
Скажем, вызывают же сами человека к оперу — так не посылать с ним команды!
(А. Солженицын, Один день из жизни Ивана Денисовича)

The fellow had long ago made himself at home in the staff quarters; he had access to the offices of the camp commandant, the man in charge of discipline, and the security officer (the Father Confessor, they called him). When working for them he sometimes beard things that even the guards didn’t know, and after a time he got a big head and came to consider scrubbing the floor for rank-and-file campguards a bit beneath him. <…>
And at once a whisper ran through the squad: Panteleyev, that son of a bitch, was staying behind again. Oh no, he wasn’t ill, the security boys were keeping him back. He’d be squealing on someone. <…>
Someone, say, is sent for by the security boys—must you take another four or five with you?
(A. Solzhenitsyn, One Day in the Life of Ivan Denisovich)


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Note added at 10 hrs (2008-02-12 10:26:25 GMT)
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Here are a few more quotations from two other Russian authors, you might also find them useful:

Спустя каких-нибудь пять минут после того, как доктор закончил свой рассказ, из ворот помещения погранотряда выехали верхами две группы оперативных сотрудников.
(В. Беляев, Старая крепость)
About five minutes after the doctor had finished his story, two groups of mounted security men rode out of headquarters.
(V. Belyaev, The Old Fortress)

- Не тот... - вздохнул оперативник. - Какой-то Кривошеин Валентин Васильевич. А по фотографии и словесному портрету - точно Кравец. <…>
Он купил в киоске сигареты, закурил и двинулся дальше. Сейчас его одолевала такая злоба, что расхотелось есть; попадись он в объятия оперативников - злоба разрядилась бы великолепной дракой.
(В. Савченко, Открытие себя)
"Not the one..." sighed the operative. "Some guy called Valentin Vasilyevich Krivoshein. But if you go by the photo and the description, he's definitely Kravets." <…>
He was engulfed in such anger that he lost his appetite, and if he had fallen into the arms of the operatives, there would have been quite a brawl.
(V. Savchenko, Self-discovery)

It was OGPU/NKVD practice to have a network of field agents covering and supervising territories
Sel'sovet - Region - Oblast and so on

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Note added at 11 hrs (2008-02-12 11:29:56 GMT)
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опер - это сокращение от "оперуполномоченный", представитель ОГПУ в населенном пункте

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Note added at 13 hrs (2008-02-12 13:45:48 GMT)
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local OGPU/NKVD agent