EVERY GROUP IS A MAXIMAL SUBGROUP OF THE FREE IDEMPOTENT GENERATED SEMIGROUP OVER A BAND
نویسندگان
چکیده
منابع مشابه
Every Group is a Maximal Subgroup of the Free Idempotent Generated Semigroup over a band
Given an arbitrary group G we construct a semigroup of idempotents (band) BG with the property that the free idempotent generated semigroup over BG has a maximal subgroup isomorphic to G. If G is finitely presented then BG is finite. This answers several questions from recent papers in the area.
متن کاملEvery Group Is a Maximal Subgroup of a Naturally Occurring Free Idempotent Generated Semigroup
The study of the free idempotent generated semigroup IG(E) over a biordered set E has recently received a deal of attention. Let G be a group, let n ∈ N with n ≥ 3 and let E be the biordered set of idempotents of the wreath product G ≀ Tn. We show, in a transparent way, that for e ∈ E lying in the minimal ideal of G ≀ Tn, the maximal subgroup of e in IG(E) is isomorphic to G. It is known that G...
متن کاملOn the Fischer-Clifford matrices of a maximal subgroup of the Lyons group Ly
The non-split extension group $overline{G} = 5^3{^.}L(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in Ly. The group $overline{G}$ in turn has L(3,5) and $5^2{:}2.A_5$ as inertia factors. The group $5^2{:}2.A_5$ is of order 3 000 and is of index 124 in L(3,5). The aim of this paper is to compute the Fischer-Clifford matrices of $overline{G}$, which together with associated parti...
متن کاملOn Maximal Subgroups of Free Idempotent Generated Semigroups
We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free...
متن کاملFree Idempotent Generated Semigroups over Bands
We study the general structure of the free idempotent generated semigroup IG(B) over an arbitrary band B. We show that IG(B) is always a weakly abundant semigroup with the congruence condition, but not necessarily abundant. We then prove that if B is a normal band or a quasi-zero band for which IG(B) satisfies Condition (P ), then IG(B) is an abundant semigroup. In consequence, if Y is a semila...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2013
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196713500100