This article is about a GAP function.
This GAP function takes as input two groups, both having a common parent group. See other GAP functions like this.
This GAP function outputs a Boolean variable, i.e., it returns either true or false. View other GAP functions with Boolean output
This function takes as input a pair of two groups, both of which have a common parent group, and returns a Boolean variable (true/false).
Suppose the first group is and the second group is .
- If, for every , is in the subgroup generated by and the conjugate , the function returns true. In particular, if , the function returns true if is an abnormal subgroup of .
- If there exists such that is not in the subgroup generated by and , the function returns false. In particular, if is a subgroup of that is not abnormal in , the function returns false.
IsAbnormal := function(G,H) return(ForAll(Set(G),g-> g in Group(Union(H,H^g)))); end;;