Equation 677 Database

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Magma 10d7491ad7e3…

magma 10d7491ad7e3
Size
656
Isomorphism class hash
10d7491ad7e35b26bd007536ce4cadf04e0bce2db18808c2afb252c7ec6c496b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 655) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 19:58:36
Display reorder
643,642,641,640,651,652,653,649,650,654,644,645,646,647,648,655,476,418,467,507,432,200,36,494,454,111,148,103,93,135,292,477,419,468,508,433,201,37,495,455,112,149,104,94,128,293,478,420,469,509,434,202,38,488,448,113,150,105,95,129,294,479,421,470,510,435,203,96,489,449,114,151,98,97,130,295,472,422,471,511,436,204,88,490,450,115,144,99,89,131,288,289,423,473,464,504,437,205,73,491,451,116,145,100,90,132,290,416,474,465,505,438,206,74,492,452,109,146,101,91,133,291,417,475,466,506,439,207,75,493,453,110,147,102,92,134,12,13,14,15,27,31,23,20,601,600,588,587,589,590,591,592,593,594,595,596,597,598,599,616,615,603,602,604,605,606,607,608,609,610,611,612,613,614,631,630,618,617,619,620,621,622,623,624,625,626,627,628,629,526,525,513,512,514,515,516,517,518,519,520,521,522,523,524,541,540,528,527,529,530,531,532,533,534,535,536,537,538,539,554,555,556,543,542,544,545,546,547,548,549,550,551,552,553,569,570,571,558,557,559,560,561,562,563,564,565,566,567,568,584,585,586,573,572,574,575,576,577,578,579,580,581,582,583,636,637,638,633,634,639,635,632,139,394,321,310,414,366,227,254,380,348,164,268,46,179,50,140,395,322,311,415,367,228,255,381,349,165,269,32,180,51,141,396,323,304,408,360,229,248,382,350,166,270,34,181,52,142,397,324,305,409,361,230,249,383,351,167,271,35,182,53,143,398,325,306,410,362,231,250,376,344,160,264,33,183,54,55,399,136,326,307,411,363,224,251,377,345,161,265,56,176,57,392,137,327,308,412,364,225,252,378,346,162,266,47,177,49,393,138,320,309,413,365,226,253,379,347,163,267,48,178,5,6,7,4,26,30,22,16,39,501,442,76,246,154,286,338,199,87,431,70,483,219,462,40,502,443,77,247,155,287,339,192,119,424,71,484,220,463,41,503,444,78,240,156,280,340,193,117,425,72,485,221,456,42,496,445,79,241,157,281,341,194,118,426,66,486,222,457,43,497,446,80,242,158,282,342,195,108,427,67,487,223,458,459,498,44,447,81,243,159,283,343,196,106,428,68,480,216,460,499,45,440,82,244,152,284,336,197,107,429,69,481,217,461,500,83,441,85,245,153,285,337,198,86,430,84,482,218,9,18,10,24,11,19,8,28,301,64,213,259,390,372,174,190,277,358,335,237,406,124,315,302,65,214,260,391,373,175,191,278,359,328,238,407,125,316,303,58,215,261,384,374,168,184,279,352,329,239,400,126,317,296,59,208,262,385,375,169,185,272,353,330,232,401,127,318,297,60,209,263,386,368,170,186,273,354,331,233,402,120,319,312,61,298,210,256,387,369,171,187,274,355,332,234,403,121,313,62,299,211,257,388,370,172,188,275,356,333,235,404,122,314,63,300,212,258,389,371,173,189,276,357,334,236,405,123,1,25,29,3,17,2,0,21 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 656 = 16 + 5*128, 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#318b3584f3b7cf7954776a978923c4aed021bf928f00ccd9dcec44330c7985ff, M = {128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143} 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, 128): MacNeish's product over GF(128); GF(128) = F_2[x]/(x^7 + 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: 16.

last edited by qawbecrdtey at 2026-10-06 19:58:37 · history