In cryptography, most practical block ciphers are E/D similar. Three core components are usually considered and combined to build E/D similar iterated block ciphers. In this report, we define a new one -the action ciphers- that extends the classical concept of group ciphers.Then we investigate a subset of action ciphers, the so-called σ-action ciphers, and give a cryptological characterization for this subset. All group ciphers are σ-action ciphers as well, but choosing a σ-action cipher which is not a group cipher eliminates "bad'" properties of group ciphers while keeping the "good" ones. Any group cipher component in any block cipher can be replaced by a σ-action cipher; such a replacement has no impact on the key-schedule algorithm.Finally, in the appendix, we show an application of these concepts that goes beyond the original scope of core components in E/D similar iterated block ciphers. Indeed we replace some group operations in IDEA by σ-action operations and get a large family of IDEA-like algorithms which can be customized.