My friend told me : federal reserve bank can lend usa banks infinity but to not make inflation fed can lend same amount of GDP , and if GDP increase fed can lend more ,, is that true that fed can lend infinity and to not make inflation fed can lend as much as GDP ?
There is a limit that the central bank can lend, but that amount is difficult to say because everyone is arguing about whether to change it. It used to be about $16.4 trillion, but now they're talking about increasing it. This restriction is an artificial one, though.
Raising the debt ceiling won't increase inflation by itself. There are 2 primary reasons that increasing government debt would contribute to inflation.
1) The higher amount that the government is paying for interest causes them to overpay for government goods, contributing to greater government spending each year (and government spending can contribute significantly to demand pull inflation)
2) The people lose confidence in the ability of the government to pay back their debt, so the government must increase interest rates in order to attract investors to the perceived increase in risk of their debt, and the increase in interest rates cause cost-push inflationary pressures through the higher cost of borrowing.
US government debt is a muddy mess right now because of the way their accounting system is arranged. With proper fiscal practices, it would be possible to determine which government debt is generating positive returns on investment, and which are generating negative ROI. Because of they way they keep track of their accounting, though, this isn't possible, so everyone ends up arguing about whether to blindly increase or decrease spending and debt, rather than cleaning up their system so that they can sort-out the bad spending while keeping the good investing.
The reason that's significant is that an investment with positive ROI will not contribute significantly to inflationary pressures since it will increase total nation value and production capacity; that means that there will be no reason for investors to lose confidence, and even though the government is being charged interest, they are still making more ROI than their interest charges, so there will be no inflation there, either. On the other hand, increasing bad spending will contribute far more greatly to inflation.
So, to answer your question, whether debt increases inflation depends on how they are spending their money. It also depends on the circumstances of the economy at the time, whether it's booming or busting, but that's for another question.