Equation 677 Database

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Magma 58459db29357…

magma 58459db29357
Size
381
Isomorphism class hash
58459db29357ab6029731eb4b024f518fa1e8d3c67eedc9410825337d58e853a
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 23:19:56
Display reorder
380,159,154,128,127,133,152,134,129,160,153,318,81,178,186,92,180,78,77,185,88,319,179,201,109,208,104,203,103,102,207,108,320,202,236,61,235,53,230,56,55,234,60,321,229,10,250,260,3,256,6,5,261,11,322,255,25,276,285,27,281,28,29,286,26,323,280,334,357,356,331,330,332,358,359,355,333,165,158,132,147,143,169,144,142,166,157,312,91,198,194,89,184,80,96,195,90,313,183,222,119,217,117,206,107,122,218,118,314,223,248,50,244,69,233,59,73,245,70,315,232,0,273,269,19,259,9,23,270,20,316,258,41,298,294,43,284,44,40,295,42,317,283,345,373,371,346,347,348,374,370,372,349,151,172,138,146,126,168,145,139,167,170,327,93,197,177,85,191,84,94,196,76,328,175,220,120,200,114,213,113,121,219,101,329,221,247,71,228,66,241,65,72,246,52,324,226,21,272,254,16,266,15,22,271,2,325,252,36,297,279,38,291,39,35,296,37,326,277,340,368,366,341,342,343,369,365,367,344,155,156,125,141,130,164,140,131,163,150,301,86,193,181,79,182,75,87,192,97,300,176,215,115,204,106,205,100,116,214,105,302,216,243,67,231,57,225,54,68,242,58,303,227,17,268,257,7,251,4,18,267,8,304,253,31,293,282,33,275,34,30,292,32,305,278,335,363,361,336,337,338,364,360,362,339,161,174,149,148,136,162,137,135,171,173,308,82,190,188,95,187,99,98,189,83,306,199,212,112,210,110,209,124,123,211,111,307,224,240,64,238,62,237,74,51,239,63,311,249,14,265,263,12,262,24,1,264,13,309,274,47,290,288,49,287,45,46,289,48,310,299,351,379,377,352,353,354,375,376,378,350 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#15bc47c2665d27cc11ae2f2ac07f8ba022379fabdb19172b737e3b8c602f9981, 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 23:19:58 · history