Asha'man on Wikipedia

The Black Tower
The Black Tower focuses much more on Battle than the Aes Sedai, but as Tarmon Gaidin has been over, and Rand al'Thor passed away, more and more divisions are occurring over the purpose of the Black Tower and the Asha'man. Since the taint is no longer there, men can channel without fear of going mad, which starts to bring up questions of whether or not another Age of Legends can be brought into power. Men and women can channel together again, and remake the greatest works of the Age of Legends.

There's a lot more possibilities now that saidin is clean: rejoining the towers, recreating the masterworks, developing new angrael, fully exploring and gaining control over Tel'aran'rhiod, recruiting male channelers, studying how saidin works, male royal councilors and advisors, and so on. A whole lot more than fighting shadowspawn is possible, and so the Asha'man are beginning to divide into smaller groups, much like the White Towers Ajahs. Time will tell if these develop into more formal divisions within the Black Tower.

Soldiers
Soldiers are the lowest rank of the Black Tower.

Dedicated
Dedicated are the middle rank of the Black Tower. They are more skilled than Soldiers, but not competent enough with saidin to be Asha'man.

Asha'man
Asha'man are full members of the Black Tower. Ranks above Asha'man are treated more like military officers than as a separate division.