Equation 677 Database

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Magma c45a18528d82…

magma c45a18528d82
Size
705
Isomorphism class hash
c45a18528d8298f2dc701dee0182913bb5ea19628e8f0a1f8616adc5d92c5fbd
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 15:54:26
Display reorder
660,250,592,273,181,270,274,248,179,271,590,272,249,591,180,269,276,253,595,177,266,277,251,593,178,267,252,275,594,176,268,279,256,587,187,261,254,588,185,280,262,589,255,186,278,260,586,259,183,282,264,584,257,184,283,265,585,258,182,281,263,687,688,686,685,143,132,347,120,154,348,144,121,152,133,349,145,131,119,153,346,142,128,116,157,344,140,129,117,155,141,345,130,118,156,353,149,138,126,160,150,139,127,354,158,137,151,125,355,159,134,148,122,352,163,135,146,123,350,161,136,147,124,351,162,703,704,701,702,563,548,243,546,574,244,564,547,572,549,242,565,550,545,573,246,562,551,542,577,247,560,552,543,575,561,245,553,544,576,241,569,554,537,580,570,555,538,239,578,556,571,536,240,579,557,568,540,237,583,558,566,541,238,581,559,567,539,236,582,671,672,670,669,394,389,43,373,357,41,392,371,358,390,42,393,391,372,356,39,397,388,369,360,40,395,386,370,361,396,38,387,368,359,34,400,380,379,363,398,381,377,32,364,382,399,378,33,362,383,403,375,37,366,384,401,376,35,367,385,402,374,36,365,679,680,678,677,445,428,104,426,409,105,443,427,407,429,106,444,430,425,408,107,441,431,422,405,108,442,432,423,406,440,109,433,424,404,110,451,434,417,415,449,435,418,111,413,436,450,416,112,414,437,447,420,113,411,438,448,421,114,412,439,446,419,115,410,692,691,690,689,508,172,51,17,214,52,506,15,212,170,50,507,171,16,213,54,511,175,13,217,55,509,173,14,215,510,53,174,12,216,49,503,167,23,220,504,168,21,47,218,169,505,22,48,219,166,502,19,45,223,164,500,20,46,221,165,501,18,44,222,699,700,698,697,78,62,2,194,98,1,79,195,99,63,0,77,64,196,100,5,74,65,197,101,3,75,66,198,102,76,4,67,199,103,8,69,60,192,96,70,61,193,6,97,59,68,191,7,95,56,72,188,11,92,57,73,189,9,93,58,71,190,10,94,663,664,662,661,634,630,294,613,596,295,632,611,597,631,293,633,629,612,598,290,637,626,609,599,291,635,627,610,600,636,292,628,608,601,285,640,621,619,602,638,622,617,286,603,620,639,618,284,604,624,643,615,288,605,625,641,616,289,606,623,642,614,287,607,682,683,684,681,659,658,225,656,657,226,651,649,648,650,224,655,654,652,653,228,529,521,519,25,229,646,645,644,647,528,227,520,518,24,231,532,525,517,28,530,526,515,232,26,527,531,516,230,27,524,535,513,234,31,522,533,514,235,29,523,534,512,233,30,695,696,693,694,476,467,208,452,491,206,477,453,492,468,207,478,469,454,493,211,479,466,455,490,209,480,464,456,488,481,210,465,457,489,203,482,473,458,497,483,474,459,204,498,475,484,460,205,499,472,485,461,202,496,470,486,462,200,494,471,487,463,201,495,667,668,665,666,312,300,90,337,324,91,313,335,325,301,89,311,299,336,323,86,308,296,333,320,87,309,297,334,321,310,88,298,332,322,81,318,306,343,330,319,307,341,82,331,305,317,342,80,329,302,314,339,84,326,303,315,340,85,327,304,316,338,83,328,675,676,673,674 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#24594adec9458e953c3b7e97dafa6bb51a67ac64efb5ebe0d91d39b768cf806c, 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 15:54:27 · history