Equation 677 Database

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Magma d81fcb7919b0…

magma d81fcb7919b0
Size
705
Isomorphism class hash
d81fcb7919b0359223ce2402036eb729b0878575448f78657c4b72081d44e325
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 21:14:40
Display reorder
660,581,592,569,557,389,582,593,390,570,558,580,594,391,568,556,584,595,388,572,560,585,596,386,573,561,583,597,387,571,559,587,598,380,575,563,588,599,381,576,564,574,586,600,382,562,590,601,383,578,566,591,602,384,579,567,589,603,385,577,565,687,688,686,685,417,429,452,441,205,418,430,206,453,442,416,428,207,454,440,420,432,204,455,444,421,433,202,456,445,419,431,203,457,443,423,435,196,458,447,424,436,197,459,448,460,422,434,198,446,426,438,199,461,450,427,439,200,462,451,425,437,201,463,449,703,704,701,702,513,523,547,535,371,511,524,372,548,536,512,525,373,549,537,509,522,370,546,534,510,520,368,544,532,508,521,369,545,533,519,529,377,553,541,517,530,378,554,542,555,518,531,379,543,515,528,376,552,540,516,526,374,550,538,514,527,375,551,539,671,672,670,669,214,472,12,478,112,215,470,113,13,476,216,471,111,14,477,217,475,108,15,481,218,473,109,16,479,219,474,110,17,480,212,467,118,18,484,213,468,119,19,482,20,211,469,117,483,208,466,114,21,487,209,464,115,22,485,210,465,116,23,486,679,680,678,677,225,235,265,248,121,223,236,122,266,249,224,237,120,267,247,221,234,124,264,244,222,232,125,262,245,220,233,123,263,246,231,241,127,256,254,229,242,128,257,255,258,230,243,126,253,227,240,130,259,250,228,238,131,260,251,226,239,129,261,252,692,691,690,689,331,343,323,146,133,332,344,134,324,144,333,345,132,322,145,330,342,136,326,149,328,340,137,327,147,329,341,135,325,148,337,349,139,321,152,338,350,140,319,150,320,339,351,138,151,336,348,142,317,155,334,346,143,318,153,335,347,141,316,154,699,700,698,697,84,105,74,68,34,85,106,35,72,66,86,107,33,73,67,87,104,30,77,71,88,102,31,75,69,89,103,32,76,70,90,96,25,80,63,91,97,26,78,64,79,92,98,24,65,93,99,28,83,62,94,100,29,81,60,95,101,27,82,61,663,664,662,661,629,642,617,605,396,630,640,397,618,606,628,641,395,616,604,632,645,392,620,608,633,643,393,621,609,631,644,394,619,607,635,648,402,623,611,636,646,403,624,612,622,634,647,401,610,638,651,398,626,614,639,649,399,627,615,637,650,400,625,613,682,683,684,681,159,358,500,490,42,157,359,43,498,491,158,360,44,499,489,156,361,45,501,488,653,652,46,654,655,657,656,47,659,658,362,356,40,504,493,363,357,41,502,494,503,364,355,39,492,365,352,36,507,496,366,353,37,505,497,367,354,38,506,495,695,696,693,694,273,285,308,297,52,271,283,53,309,295,272,284,51,307,296,269,281,48,304,293,270,282,49,305,294,268,280,50,306,292,279,291,58,314,303,277,289,59,315,301,313,278,290,57,302,275,287,54,310,299,276,288,55,311,300,274,286,56,312,298,667,668,665,666,175,187,167,4,409,176,188,407,168,5,177,189,408,166,3,174,186,405,170,1,172,184,406,171,0,173,185,404,169,2,181,193,415,165,10,182,194,413,163,11,164,183,195,414,9,180,192,411,161,6,178,190,412,162,7,179,191,410,160,8,675,676,673,674 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#e0ddb86ffdf58ba66baf4adb67528755a1dfe5eefeff33f7cfcb062fa9d34ece, 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 21:14:41 · history