Equation 677 Database

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Magma 1231919492cb…

magma 1231919492cb
Size
705
Isomorphism class hash
1231919492cbe63078f21ddd15a41b9c4cb8608d0653c8ac4d48812bb8fdb20c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 20:02:30
Display reorder
660,296,633,602,617,624,294,625,634,603,618,632,623,295,604,619,636,299,620,605,616,637,297,621,606,614,607,635,298,622,615,302,600,630,639,608,300,601,631,640,609,301,599,629,638,610,596,305,626,642,611,597,303,627,643,612,598,304,628,641,613,687,688,686,685,235,348,363,371,388,236,389,349,364,369,350,387,234,365,370,351,238,384,362,367,352,239,385,360,368,361,353,237,386,366,241,354,379,346,377,242,355,380,347,375,240,356,378,345,376,357,244,382,342,373,358,245,383,343,374,359,243,381,344,372,703,704,701,702,289,560,576,586,552,290,553,561,577,584,562,551,288,575,585,563,292,548,572,589,564,293,549,573,587,574,565,291,550,588,287,582,558,566,592,285,583,559,567,590,286,581,557,568,591,578,283,554,569,595,579,284,555,570,593,580,282,556,571,594,671,672,670,669,114,4,252,396,34,115,35,11,253,397,3,33,116,254,398,1,117,30,255,399,0,118,31,256,400,257,2,119,32,401,120,250,25,10,394,121,251,26,8,395,122,249,24,9,393,246,123,28,6,390,247,124,29,7,391,248,125,27,5,392,679,680,678,677,258,440,406,415,430,259,431,438,407,416,439,429,260,405,414,443,261,426,402,418,441,262,427,403,419,404,442,263,428,417,264,412,436,446,421,265,413,437,444,422,266,411,435,445,420,408,267,432,449,424,409,268,433,447,425,410,269,434,448,423,692,691,690,689,506,172,135,141,206,504,204,173,136,142,171,205,505,137,143,168,509,209,134,140,169,507,207,132,138,133,170,508,208,139,501,126,201,163,147,502,127,202,164,148,503,128,203,162,149,129,500,200,166,146,130,498,198,167,144,131,499,199,165,145,699,700,698,697,17,86,106,54,80,15,78,84,107,55,85,79,16,105,56,89,13,83,102,57,87,14,81,103,58,104,88,12,82,59,23,97,75,92,52,21,98,76,90,53,22,96,77,91,51,100,19,74,95,48,101,20,72,93,49,99,18,73,94,50,663,664,662,661,646,161,180,312,213,644,214,159,181,313,160,215,645,182,314,157,649,212,183,315,158,647,210,184,316,185,156,648,211,317,652,178,219,152,310,650,179,220,150,311,651,177,221,151,309,174,655,218,155,306,175,653,216,153,307,176,654,217,154,308,682,683,684,681,44,523,529,539,517,42,518,524,530,540,525,516,43,528,541,522,47,520,526,538,657,45,656,658,659,527,521,46,519,537,39,535,515,108,545,40,536,513,109,546,41,534,514,110,547,531,38,511,111,544,532,36,512,112,542,533,37,510,113,543,695,696,693,694,272,472,475,489,456,270,457,473,476,490,471,458,271,474,491,468,275,459,478,488,469,273,460,479,486,477,470,274,461,487,278,481,454,463,495,276,482,455,464,496,277,480,453,462,497,484,281,450,466,494,485,279,451,467,492,483,280,452,465,493,667,668,665,666,65,187,326,332,227,63,225,188,324,330,186,226,64,325,331,190,61,223,329,335,191,62,224,327,333,328,189,60,222,334,71,321,233,193,338,69,322,231,194,336,70,323,232,192,337,320,67,229,196,341,318,68,230,197,339,319,66,228,195,340,675,676,673,674 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#b87a44718af64d04bd4c9a05b8565b67306fb6d5f63754d3fbad663d9bf67702, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 20:02:31 · history