Equation 677 Database

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Magma c7b4a2472f3f…

magma c7b4a2472f3f
Size
705
Isomorphism class hash
c7b4a2472f3fa348b4bdf99d59818bc2045f4cacd2adad7db336e70ee0e6f649
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 21:23:24
Display reorder
660,347,270,523,428,394,348,268,521,426,392,349,269,427,522,393,346,273,526,431,397,344,271,524,429,395,345,272,525,430,396,265,353,529,434,400,266,354,527,432,398,267,355,528,433,399,352,264,532,437,403,350,262,530,435,401,351,263,531,436,402,674,681,676,677,65,230,209,71,535,66,231,210,72,533,67,229,73,208,534,68,226,212,74,538,69,227,213,75,536,70,228,211,76,537,236,63,207,77,541,237,64,205,78,539,235,62,206,79,540,59,232,203,80,544,60,233,204,81,542,61,234,202,82,543,662,672,665,668,594,243,499,382,100,592,241,497,380,98,593,242,381,498,99,597,239,502,385,96,595,240,500,383,97,596,238,501,384,95,249,600,505,388,106,247,598,503,386,104,248,599,504,387,105,603,245,508,391,102,601,246,506,389,103,602,244,507,390,101,686,680,683,675,326,7,464,182,406,327,8,462,183,404,328,6,184,463,405,329,10,467,181,409,330,11,465,179,407,331,9,466,180,408,5,324,470,188,412,3,325,468,189,410,4,323,469,187,411,653,0,655,656,657,321,2,471,185,413,322,1,472,186,414,703,699,704,698,23,54,358,606,511,21,55,356,604,509,22,53,605,357,510,19,57,361,609,514,20,58,359,607,512,18,56,360,608,513,52,14,364,612,517,50,12,362,610,515,51,13,363,611,516,17,48,367,615,520,15,49,365,613,518,16,47,366,614,519,691,690,692,694,487,168,123,117,582,485,169,124,118,580,486,167,116,122,581,490,171,119,113,585,488,172,120,114,583,489,170,121,115,584,174,493,129,108,588,175,491,130,109,586,173,492,128,107,587,496,177,125,111,591,494,178,126,112,589,495,176,127,110,590,664,666,669,670,286,147,547,302,283,287,148,545,303,284,288,146,301,546,285,289,143,550,298,282,290,144,548,299,280,291,145,549,300,281,153,292,553,308,274,154,293,551,309,275,152,294,552,307,276,295,149,556,304,277,296,150,554,305,278,297,151,555,306,279,695,693,696,689,161,256,642,370,440,162,257,640,368,438,163,258,369,641,439,164,259,645,373,443,165,260,643,371,441,166,261,644,372,442,254,159,648,376,446,255,160,646,374,444,253,158,647,375,445,155,250,651,379,449,156,251,649,377,447,157,252,650,378,448,685,688,678,673,571,223,29,312,417,569,224,30,310,415,570,225,311,31,416,574,222,32,315,420,572,220,33,313,418,573,221,34,314,419,214,577,27,318,423,215,575,28,316,421,216,576,26,317,422,659,217,658,652,654,578,218,24,319,424,579,219,25,320,425,701,702,697,700,46,199,475,559,630,44,200,473,557,628,45,201,558,474,629,42,198,478,562,633,43,196,476,560,631,41,197,477,561,632,190,37,481,565,636,191,35,479,563,634,192,36,480,564,635,40,193,484,568,639,38,194,482,566,637,39,195,483,567,638,661,663,671,667,136,94,336,618,452,134,92,337,616,450,135,93,617,335,451,132,90,332,621,455,133,91,333,619,453,131,89,334,620,454,85,142,342,624,458,83,140,343,622,456,84,141,341,623,457,138,88,338,627,461,139,86,339,625,459,137,87,340,626,460,682,684,679,687 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#edd749230bc58665165cb5ff86cf593765d0cefcd490b689f1cd7ce77c95b856, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 21:23:25 · history