Nazis admitted Holocaust before Nurnberg trials

this article about Holocaust denial. Much more is documented in Irving v Lipstadt.
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In 1922, Hitler told a journalist that: "Once I really am in power, my first and foremost task will be the annihilation of the Jews. As soon as I have the power to do so, I will have gallows built in rows - at the Marienplatz in Munich, for example - as many as traffic allows. Then the Jews will be hanged indiscriminately, and they will remain hanging until they stink; they will hang there as long as the principles of hygiene permit. As soon as they have been untied, the next batch will be strung up, and so on down the line, until the last Jew in Munich has been exterminated. Other cities will follow suit, precisely in this fashion, until all Germany has been completely cleansed of Jews." --Adolf Hitler, 1922. (Translation from Nizkor)

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In 1943 Himmler spoke openly about the extermination of the Jewish people, as well as the equivocation used to cover it up, during a speech to SS Officers. An audio recording, as well as a transcription of the original German, is available on this website.

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I also want to mention a very difficult subject before you here, completely openly.
It should be discussed amongst us, and yet, nevertheless, we will never speak about it in public.
Just as we did not hesitate on June 30 to carry out our duty, as ordered, and stand comrades who had failed against the wall and shoot them.
About which we have never spoken, and never will speak.
That was, thank God, a kind of tact natural to us, a foregone conclusion of that tact, that we have never conversed about it amongst ourselves, never spoken about it, everyone shuddered, and everyone was clear that the next time, he would do the same thing again, if it were commanded and necessary.
I am talking about the "Jewish evacuation": the extermination of the Jewish people.
It is one of those things that is easily said. "The Jewish people is being exterminated," every Party member will tell you, "perfectly clear, it's part of our plans, we're eliminating the Jews, exterminating them, ha!, a small matter."
And then along they all come, all the 80 million upright Germans, and each one has his decent Jew. They say: all the others are swine, but here is a first-class Jew.
And none of them has seen it, has endured it. Most of you will know what it means when 100 bodies lie together, when there are 500, or when there are 1000. And to have seen this through, and -- with the exception of human weaknesses -- to have remained decent, has made us hard and is a page of glory never mentioned and never to be mentioned.
Because we know how difficult things would be, if today in every city during the bomb attacks, the burdens of war and the privations, we still had Jews as secret saboteurs, agitators and instigators. We would probably be at the same stage as 1916-17, if the Jews still resided in the body of the German people.
We have taken away the riches that they had, and I have given a strict order, which Obergruppenführer Pohl has carried out, we have delivered these riches completely to the Reich, to the State. We have taken nothing from them for ourselves. A few, who have offended against this, will be [judged] in accordance with an order, that I gave at the beginning: He who takes even one Mark of this is a dead man.
A number of SS men have offended against this order. There are not very many, and they will be dead men - WITHOUT MERCY! We have the moral right, we had the duty to our people to do it, to kill this people who wanted to kill us. But we do not have the right to enrich ourselves with even one fur, with one Mark, with one cigarette, with one watch, with anything. That we do not have. Because at the end of this, we don't want, because we exterminated the bacillus, to become sick and die from the same bacillus.
I will never see it happen, that even one bit of putrefaction comes in contact with us, or takes root in us. On the contrary, where it might try to take root, we will burn it out together. But altogether we can say: We have carried out this most difficult task for the love of our people. And we have taken on no defect within us, in our soul, or in our character.

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2 days later in another speech, Himmler said:

"We came to the question: what to with the women and children? I decided to find a clear solution here as well. I did not consider myself justified to exterminate the men - that is, to kill them or have them killed - and allow the avengers of our sons and grandsons in the form of their children to grow up. The difficult decision had to be taken to make this people disappear from the earth. For the organisation which had to execute this task, it was the most difficult which we had ever had. But it was accomplished, and without -- I believe I can say -- our men and their leaders suffering any mental or spiritual damage."

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On 29 December 1942, Himmler presented Hitler with the "report to the Fuhrer on fighting against gangs", No. 51.1 This report, which covered the period from August to November, 1942, and which referred only to a part of the occupied Soviet area (southern Russia, Ukraine and the district of Bialystok); included the following numbers concerning persons imprisoned or executed:

  1. Bandits
         * a)established number of deaths after combat 1.337
         * b)prisoners executed immediately 737
         * c)prisoners executed after lengthy thorough interrogation 7.828
  2. Gang helpers and suspects
         * a)arrested 16.553
         * b)executed 14.257
         * c)Jews executed 363.211