This Allahu Akbar - Allah Akbar as can also be reported - when a terrorist yells it, reporters will say it means "God is great."

But does it not really mean, "Allah is the greatest?"  Or, "Allah is the one god?"

In other words, Allah is the only god, better than "your" God - he is the supreme god...?

Don't they really misinterpret it?  It is a war cry, a challenge to Christians.

Reporters, news people, DZ.  I assumed you were smart enough to know that without me spelling it out.  My mistake.

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I heard on reliable testimony that a priest performing an exorcism demanded of the devil under subjection that he reveal what his name is and the devil replied that his name is "Allah." In that context a possessing devil is not able to lie, and must divulge his real name.
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Being in power of the Church to BIND the devil, the priest then made the devil promise to demonstrate some time in the future when the priest would invoke him to show his effect on other people. This was done during the exorcism, and the exorcism was completed effectively.
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A few weeks later, the same priest was in Saudi Arabia overlooking a public square with hundreds of people walking around in the area before him as he looked out upon them from a higher level, out of a window. The priest invoked the devil he had exorcised by name, commanding him to show his power over all those people walking to and fro outside in the plaza. Immediately, all the walking people stopped in their tracks, and turned to stare for a second or two in the direction of the priest up in that window. Then they all turned forward again and resumed their walking as though they were entirely unaware of having paused just then.
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Think of it as a flash mob acting on cue, but without having planned on doing so.
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The priest was convinced of the power Allah the devil has over people of that region and it should never be underestimated, for they know not what influence it is that they are under.
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Allah: The name of God in Arabic 

• Etymology/Composition of: It is a compound word from the article, ‘al, and ilah, divinity, and signifies “the god” par excellence. 
  

This form of the divine name is in itself a sure proof that ilah was at one time an appellative, common to all the local and tribal gods. Gradually, with the addition of the article, it was restricted to one of them who took precedence of the others; finally, with the triumph of monotheism, He was recognized as the only true God. 

In one form or another this Hebrew root occurs in all Semitic languages as a designation of the Divinity; but whether it was originally a proper name, pointing to a primitive monotheism, with subsequent deviation into polytheism and further rehabilitation, or was from the beginning an appellative which became a proper name only when the Semites had reached monotheism is a much debated question. 

It is certain, however, that before the time of Mohammed, owing to their contact with Jєωs and Christians, the Arabs were generally monotheists. 

The notion of Allah in Arabic theology is substantially the same as that of God among the Jєωs, and also among the Christians, with the exception of the Trinity, which is positively excluded in the Koran, cxii: “Say God, is one God, the eternal God, he begetteth not, neither is he begotten and there is not any one like unto him.” 

His attributes denied by the heterodox Motazilites, are ninety-nine in number. Each one of them is represented by a bead in the Moslem chaplet, while on the one hundredth and larger bead, the name of Allah itself is pronounced. 

It is preposterous to assert with Curtiss (Ursemitische Religion, 119) that the nomadic tribes of Arabia, consider seriously the Oum-el-Gheith, “mother of the rain,” as the bride of Allah and even if the expression were used such symbolical language would not impair, in the least, the purity of monotheism held by those tribes.^[1] 
Let it be noted that although Allah is an Arabic term, it is used by all Moslems, whatever be their language, as the name of God. 

R. BUTIN^[2] [3] 

References

• ^  1. (Cf. Revue Biblique, Oct., 1906, 580 sqq.)
• ^  2. Entry: Allah f/ "THE CATHOLIC ENCYCLOPEDIA: AN INTERNATIONAL WORK OF REFERENCE ON THE CONSTITUTION, DOCTRINE, DISCIPLINE, AND HISTORY OF THE CATHOLIC CHURCH" by Herbermann, Charles G. © 1907 to 1914 Encyclopedia Press, Inc., New York, US. CENSOR / NIHIL OBSTAT: NOVEMBER 1, 1907 REMY LAFORT, S.T.D. IMPRIMATUR: +JOHN CARDINAL FARLEY ARCHBISHOP OF NEW YORK