Equation 677 Database

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Magma 3727b0b893ff…

magma 3727b0b893ff
Size
381
Isomorphism class hash
3727b0b893ff43e952bc6560430a94caf3ecebea9e9abb8891b10ee47e5b0e3d
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:43:59
Display reorder
380,237,85,219,138,120,121,238,86,220,141,122,239,87,221,139,234,123,88,216,142,235,124,89,217,143,84,125,236,218,140,69,319,247,101,274,70,320,248,96,275,71,317,249,97,270,66,318,250,98,271,67,300,251,99,272,68,329,246,100,273,289,290,291,292,293,288,360,336,338,361,337,335,362,363,339,359,176,24,180,75,14,15,177,25,181,76,16,178,26,182,77,179,17,27,183,72,174,12,28,184,73,29,13,175,185,74,30,308,257,105,162,31,310,252,106,163,32,327,253,107,164,33,306,254,102,165,34,328,255,103,166,35,307,256,104,167,227,223,224,225,226,222,374,342,344,365,343,341,366,367,345,364,278,130,258,52,148,149,279,131,259,53,145,280,126,260,48,281,144,127,261,49,276,146,128,262,50,129,147,277,263,51,108,325,170,22,299,109,326,171,23,296,110,321,172,18,294,111,322,173,19,298,112,323,168,20,297,113,324,169,21,295,198,200,201,202,203,199,368,346,348,369,347,350,370,371,349,372,157,9,195,134,116,117,158,10,196,135,118,159,11,197,136,160,119,6,192,137,161,114,7,193,132,8,115,156,194,133,45,301,240,92,264,46,309,241,93,265,47,302,242,94,266,42,304,243,95,267,43,303,244,90,268,44,305,245,91,269,284,286,287,282,283,285,357,333,351,358,334,352,356,373,332,355,229,81,204,62,0,2,230,82,205,63,3,231,83,206,64,232,4,78,207,65,233,5,79,208,60,80,1,228,209,61,54,316,188,40,155,55,311,189,41,151,56,312,190,36,150,57,313,191,37,152,58,314,186,38,153,59,315,187,39,154,212,214,215,210,211,213,376,354,330,379,353,340,378,375,331,377 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#cf33a750fb5380e864feffa0a66933b1b75aafed19df5d2b70e6e1ac9aa6bb80, 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 23:44:00 · history