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Yes. Any of the component letters of SAM is ...

AorM....

Meanwhile I am pretty sure that I have got the four group messages and the three letters.

I had assumed that the word common to groups 1 and 3 relates to the direction of entry.

But I do not see how such a interpretation would work , given for example that the 3 letter words are in groups 2 and 4

I have group 4 described by a the extras in group 3. On a strict, mathematical interpretation that would lead to non-letters.

A hint would be appreciated

I meant 2 and 3 for the 3 letter words

Woodlouse, you need to consider the misprints. They should help you understand how to interpret the four-letter word common to two of the instructions.

But doesn't AM or S leave 'r', not 'o', as the extra letter from the answer?

No. Spelt like that, ‘r’ would be a missing letter. The word or is repeated, and ‘o’ becomes extra

Thanks Quisling I can see the transformations that you have to apply to the individual letters. So I get the idea.

I had thought that one would apply the same processes mutatis mutandis to whole words.

I am now wondering if the instructions normally apply to whole words but occasionally individual letters

Oops. I'll get my coat. Thanks.

Not so, woodlouse. But that’s where the fun begins. A line of symmetry, as a way of representing an instruction, could be very long or very short depending on an answer’s orientation.

Good quality hint, Quisling

I will press on.