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Jan
22
awarded  Organizer
Jan
22
revised subsets of groups which have to be closed no matter what
arXiv's tags added
Jan
22
suggested approved edit on subsets of groups which have to be closed no matter what
Jan
22
awarded  Nice Answer
Jan
22
answered subsets of groups which have to be closed no matter what
Jan
21
revised Fantastic properties of Z/2Z
added 12 characters in body
Jan
21
answered Fantastic properties of Z/2Z
Jan
21
answered Examples of cancellative normal semigroups
Jan
20
comment Why the axiomatic rank of the variety of groups is equal to three?
Your octonion argument is much simpler and works perfectly. The algebra of all unit octonions or all non-zero octonions (with operations $\cdot$, ${\ }^{-1}$, and $1$) is non-associative but satisfies all two-variable laws that are consequences of the group axioms.
Jan
19
answered Non finitely based varieties of groups defined by finitely many variables
Jan
17
comment Almost uniquely generated groups
Oh yes, thank you!
Jan
17
awarded  Citizen Patrol
Jan
17
comment Almost uniquely generated groups
"Any finite $p$-group which is relatively free in some variety has this property by the same argument. In light of Geoff's answer perhaps these are the only ones?" -- No. The quaternion group of order 8 is not relatively free but satisfies the conditions.
Jan
17
comment Almost uniquely generated groups
Why $\{a_{1},b_{1},g_{2},g_{3}, \ldots, g_{n} \}$ is irredundant?
Jan
17
comment Almost uniquely generated groups
No. $S$ is unique up to automorphisms; so, the complement of $S$ is not necessary the Frattini subgroup.Take a cyclic group of prime order, for example.
Jan
16
comment Almost uniquely generated groups
Yes. And probably you mean Question 2 as you use that the orders are finite.
Jan
16
comment Almost uniquely generated groups
This condition is indeed weaker. See the (wrong) answer of M. Shahryari.
Jan
16
comment Almost uniquely generated groups
No. Even $F_1$ does not satisfy. The question is about inclusion-minimal sets.
Jan
16
comment Almost uniquely generated groups
It seems that you use the letter $n$ in two different senses. You are talking about $m$-generated free groups in the varieties of nilpotent groups of exponent $p^n$, right?
Jan
16
asked Almost uniquely generated groups