**Core Concept**
Fat necrosis is a form of traumatic fat tissue damage that occurs as a result of severe blunt trauma to the breast, leading to the release of lipase enzymes. This process results in the accumulation of fatty acids, which subsequently precipitate out of solution to form calcium soaps, causing firm, painless lumps.

**Why the Correct Answer is Right**
The patient's history of traumatic blow to the breast, followed by the development of a firm, painless lump, is highly suggestive of fat necrosis. This condition typically occurs when there is significant trauma to the breast, leading to the rupture of fat cells and the release of lipase enzymes. The lipase enzymes break down the triglycerides in the fat cells into fatty acids and glycerol. The fatty acids then combine with calcium ions to form calcium soaps, which accumulate in the breast tissue and cause the characteristic firm lumps.

**Why Each Wrong Option is Incorrect**
**Option A:** An abscess would typically present with signs of infection, such as redness, warmth, and tenderness, which are not present in this case.
**Option C:** Fibroadenoma is a common benign tumor of the breast, but it is typically smooth and mobile, and not associated with a history of trauma.
**Option D:** Inflammatory carcinoma is a rare and aggressive form of breast cancer that presents with diffuse breast erythema and edema, which is not consistent with the patient's presentation.

**Clinical Pearl / High-Yield Fact**
Fat necrosis can mimic breast cancer clinically and radiologically, making it an important consideration in the differential diagnosis of breast masses. It is often associated with a history of trauma, and the characteristic firm, painless lumps can be differentiated from cancer by their lack of mobility and absence of nipple retraction.

**✓ Correct Answer: B. Fat necrosis**