Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 9b09b962e8e1…

magma 9b09b962e8e1
Size
381
Isomorphism class hash
9b09b962e8e1f7eefb73e17e7514855a1226ec19289d3581bad8721e291e5b9d
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 23:37:26
Display reorder
380,14,273,15,213,12,13,58,63,68,48,53,243,288,233,238,228,218,223,98,293,103,108,113,118,28,33,23,40,298,35,278,263,268,258,248,253,168,173,178,153,158,163,283,73,78,93,82,88,143,148,138,128,133,123,183,188,193,198,203,208,325,324,326,327,328,329,333,358,368,348,343,354,338,363,373,378,10,272,11,212,8,9,57,62,67,47,52,240,287,232,237,227,217,222,97,292,102,107,112,117,27,32,22,43,297,38,277,262,267,255,246,250,167,172,177,152,157,162,281,72,75,92,81,87,142,147,137,127,132,122,182,187,192,197,202,207,301,302,300,305,303,304,332,357,367,347,342,352,337,362,372,377,3,271,2,210,0,1,56,61,66,45,50,242,285,230,235,226,216,221,95,291,101,105,110,115,25,30,21,41,296,36,276,261,266,257,247,252,166,171,176,151,156,161,282,71,77,90,84,85,140,145,135,126,131,121,180,185,190,196,201,206,322,321,323,318,319,320,331,356,365,345,341,351,335,361,370,375,17,274,18,214,19,16,59,64,69,49,54,244,289,234,239,229,219,224,99,294,104,109,114,119,29,34,24,44,299,39,279,264,269,259,249,254,169,174,179,154,159,164,284,74,79,94,83,89,144,149,139,129,134,124,184,189,194,199,204,209,306,308,307,311,309,310,334,359,369,349,344,353,339,364,374,379,6,270,7,211,4,5,55,60,65,46,51,241,286,231,236,225,215,220,96,290,100,106,111,116,26,31,20,42,295,37,275,260,265,256,245,251,165,170,175,150,155,160,280,70,76,91,80,86,141,146,136,125,130,120,181,186,191,195,200,205,312,314,313,317,315,316,330,355,366,346,340,350,336,360,371,376 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#9f798321a12a7c259b4293859981bcb696138223932c95126c1c0ef29c354b2f, M = {66} 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 23:37:27 · history