Equation 677 Database

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Magma 7f3f3c6fdebc…

magma 7f3f3c6fdebc
Size
381
Isomorphism class hash
7f3f3c6fdebcd1ba7ec084b9b61e5e3fcc9e0d81fa220ab4278ce9f65ebc26ef
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 23:37:50
Display reorder
380,118,113,293,98,103,107,141,145,137,127,131,120,220,2,281,23,24,25,278,288,273,263,268,258,32,210,31,29,30,28,181,186,191,195,200,205,160,150,155,176,166,171,311,309,310,308,306,307,76,250,71,93,82,88,22,216,7,8,9,10,226,236,232,296,241,246,356,341,335,330,345,368,352,361,375,371,119,114,294,99,104,108,144,149,139,129,134,124,222,47,282,44,45,46,279,289,274,264,269,259,37,212,36,35,38,34,180,185,190,196,201,206,164,154,159,179,169,174,316,317,315,313,314,312,79,254,74,94,84,89,43,217,42,40,41,39,227,237,233,297,242,247,357,342,337,331,347,369,354,364,378,374,117,112,292,95,100,109,140,148,135,125,130,121,221,26,280,11,27,12,276,286,271,262,266,256,13,211,33,15,16,14,184,189,194,199,204,209,163,153,158,178,168,173,320,318,319,323,321,322,75,251,70,91,81,87,21,215,20,18,19,17,225,235,230,295,240,245,355,340,336,334,346,366,350,363,376,373,116,110,290,97,102,106,143,147,138,128,133,123,223,48,283,4,49,3,275,285,270,261,265,257,63,214,62,6,64,5,183,188,193,198,203,208,162,152,157,177,167,172,326,324,325,329,327,328,77,252,72,92,80,86,68,219,67,69,66,65,228,238,231,298,243,248,358,344,339,333,348,365,353,362,379,372,115,111,291,96,101,105,142,146,136,126,132,122,224,61,284,60,58,59,277,287,272,260,267,255,51,213,50,0,52,1,182,187,192,197,202,207,161,151,156,175,165,170,304,305,303,300,302,301,78,253,73,90,83,85,56,218,55,57,54,53,229,239,234,299,244,249,359,343,338,332,349,367,351,360,377,370 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 = {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 23:37:51 · history