Equation 677 Database

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Magma 4b2f14cbb02d…

magma 4b2f14cbb02d
Size
707
Isomorphism class hash
4b2f14cbb02dce47134ea94ce06513536796d441e3a83aedf81ca523497a5d4e
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 18:34:54
Display reorder
229,228,230,231,232,233,706,292,291,293,288,289,290,41,36,37,38,39,40,196,195,197,192,193,194,73,72,74,75,76,77,284,283,285,286,287,282,261,260,262,263,258,259,213,212,214,215,210,211,169,168,170,171,172,173,302,300,303,304,305,301,298,299,294,296,297,295,530,532,531,527,528,529,354,356,355,359,357,358,547,546,548,549,550,551,403,402,404,405,406,407,417,419,418,414,415,416,324,326,325,329,327,328,456,457,533,460,458,459,469,468,467,471,472,470,494,496,495,493,491,492,561,563,562,559,558,560,608,617,606,611,618,607,642,625,640,638,700,677,694,703,698,680,699,704,705,702,96,101,97,98,99,100,85,86,87,88,89,84,61,60,62,63,64,65,105,104,106,107,102,103,128,127,129,130,131,126,118,117,119,114,115,116,159,158,160,161,156,157,251,250,246,247,248,249,269,268,265,264,266,267,154,153,155,150,151,152,534,536,535,537,538,539,480,479,481,482,483,484,386,385,384,388,389,387,349,348,350,351,352,353,516,515,517,519,520,518,376,375,377,372,373,374,379,378,380,381,382,383,507,506,508,503,504,505,573,575,574,572,571,570,555,556,552,553,554,557,633,634,631,632,630,610,635,615,629,637,701,693,695,683,669,666,675,674,684,685,270,271,272,273,274,275,52,53,48,49,50,51,18,23,19,20,21,22,45,44,46,47,42,43,58,57,59,54,55,56,165,164,166,167,162,163,71,70,66,67,68,69,136,135,137,132,133,134,95,94,90,91,92,93,83,82,78,79,80,81,400,399,401,397,398,396,393,395,394,392,390,391,453,455,454,452,450,451,477,476,478,473,474,475,310,309,311,306,308,307,316,315,317,312,313,314,444,446,445,449,447,448,423,425,424,422,420,421,567,565,566,564,569,568,545,544,543,542,540,541,613,627,626,614,612,628,639,616,641,636,691,692,679,686,665,671,670,687,678,696,276,277,278,279,280,281,138,139,140,141,142,143,31,30,32,33,34,35,28,27,29,24,25,26,148,147,149,144,145,146,238,237,239,234,235,236,122,121,123,124,125,120,241,240,242,243,244,245,257,256,252,253,254,255,113,112,108,109,110,111,433,432,434,436,437,435,601,602,600,605,603,604,441,443,442,440,438,439,428,427,426,430,431,429,577,578,576,579,580,581,365,364,363,361,362,360,586,585,587,583,582,584,595,596,594,599,597,598,511,510,509,513,514,512,589,590,588,591,592,593,647,644,648,645,646,643,651,653,650,654,697,676,681,690,672,667,673,689,682,688,7,6,8,9,10,11,205,206,207,208,209,204,227,226,222,223,224,225,178,177,179,174,175,176,186,191,187,188,189,190,184,183,185,180,181,182,202,201,203,198,199,200,5,4,1,0,2,3,221,220,216,217,218,219,16,15,17,12,13,14,370,369,371,367,368,366,502,501,500,498,499,497,522,521,523,524,525,526,464,466,465,463,461,462,410,409,408,413,411,412,332,331,330,334,335,333,343,342,344,345,346,347,319,318,320,321,322,323,338,337,336,340,341,339,490,489,488,487,485,486,621,649,609,619,620,622,652,623,624,655,664,659,661,663,657,656,658,660,662,668 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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#5ad34b2f8758383b4965947b4701d5813e2a88f030dcc851453e9c1dba339352, M = {12, 13, 14, 15, 16, 17, 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, 140): MacNeish's product over GF(4) x GF(5) x GF(7); 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: 101.

last edited by qawbecrdtey at 2026-10-08 18:34:55 · history