problem in understanding a paper about automorphism in p-groups

Question

I was trying to read "NON-INNER AUTOMORPHISMS OF ORDER p IN FINITE p-GROUPS OF COCLASS 3" by MARCO RUSCITTI, LEIRE LEGARRETA, AND MANOJ K. YADAV but found few theorem confusing
in page 5 Definition 3.1 we have

after few lemmas and remarks
Then in page 8 we have Theorem 4.1

then Arthur say that Hypothesis B is much stronger than Hypothesis A and every all the results proved in the preceding section under Hypothesis A are also true under Hypothesis B.
confusing part is that in Hypothesis A we have $=$ but in theorem 4.1 part (i) we have $\not =$ so we cant above result
so is there is a typo or i missing some thing?

Answer 1

"None of these things holding" means the first one (i) doesn't, which means Hyp A holds. Hence Hyp B implies Hyp A, so B is indeed stronger.