Be patient and pups will appear when the plant is ready

Sounds like you have an Aechmea fasciata,a very common bromeliad in most stores and nurseries these days.An easy plant to care for as well.When the pink bloom spike has dried out,best to remove it as close to the center cup as you can,and then wait until the plant begins to produce offsets,[pups]which may take a few months. Meanwhile,do not provide water in the cup,as it can produce conditions that may cause the plant to rot at the base. Misting,or light spraying is ok. Let the soil nearly dry out until watering again,and keep the plant in bright light,or morning and late afternoon sun.Outer lower leaves may dry out and turn brown,and for appearences,they can be removed.This is normal for a plant that has bloomed.Eventually,after the pups are about half the size of the original plant,the original can be removed by cutting it off level to the soil,if thats what you prefer,and the pups will grow to full size,and eventually flower.A lot of helpful information is available on the website,www.fcbs.org .Bob

Thanks for the encouragement and the great instructions!