Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma c244c1f4e5ed…

magma c244c1f4e5ed
Size
381
Isomorphism class hash
c244c1f4e5ed556c63702fa61cfa4a007494f9eeb0513c6217e412607fa906a0
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:25:11
Display reorder
380,30,55,35,40,45,50,325,326,327,328,329,324,65,71,76,81,86,60,131,136,141,146,120,126,6,7,8,9,10,11,195,200,205,181,186,191,255,261,266,240,245,250,291,296,270,275,280,286,155,160,166,171,176,150,210,220,236,225,231,215,100,111,95,116,90,106,335,339,357,371,376,351,345,333,368,364,34,59,39,44,48,53,310,311,306,307,308,309,69,74,79,84,89,64,133,139,144,149,124,129,28,19,21,23,25,26,199,203,208,183,189,194,259,264,269,244,248,253,294,299,274,278,284,289,158,163,168,174,178,153,214,223,239,229,234,218,103,114,98,118,93,108,331,349,359,373,378,353,342,337,366,361,31,56,36,41,46,51,303,304,305,301,300,302,67,72,77,82,87,62,130,135,140,145,121,125,16,17,12,13,14,15,196,201,206,180,185,190,256,260,265,241,246,251,290,295,271,276,281,285,156,161,165,170,175,151,211,221,235,226,230,216,101,110,96,115,91,105,336,344,355,372,377,354,347,346,365,362,33,58,38,43,49,54,317,312,313,314,315,316,66,70,75,80,85,61,134,138,143,148,123,128,29,18,20,22,24,27,198,204,209,184,188,193,258,263,268,243,249,254,293,298,273,279,283,288,159,164,169,173,179,154,213,224,238,228,233,219,104,113,99,119,94,109,341,343,358,374,379,352,332,338,367,360,32,57,37,42,47,52,321,322,323,318,319,320,68,73,78,83,88,63,132,137,142,147,122,127,4,5,1,0,2,3,197,202,207,182,187,192,257,262,267,242,247,252,292,297,272,277,282,287,157,162,167,172,177,152,212,222,237,227,232,217,102,112,97,117,92,107,348,330,356,370,375,350,334,340,369,363 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#4ff69c35f55aa106c20b4528e074e3f72eddedd150e00069ea529e91bc9e2010, M = {71} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 51.

last edited by qawbecrdtey at 2026-10-01 23:25:12 · history