Equation 677 Database

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Magma c9e4496467cd…

magma c9e4496467cd
Size
705
Isomorphism class hash
c9e4496467cd1b20c1ae8f25e4abb3bd5f50ebad9084ac4f11cb0bbf343cf2a3
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 20:02:05
Display reorder
704,255,257,256,253,254,252,263,261,262,259,260,258,273,274,275,272,270,271,264,265,266,267,268,269,236,234,235,239,237,238,231,232,233,230,228,229,247,248,246,250,251,249,245,243,244,241,242,240,581,579,580,577,578,576,587,585,586,583,584,582,670,684,679,688,443,442,441,438,439,440,433,434,432,436,437,435,452,450,451,455,453,454,447,448,449,446,444,445,68,66,67,71,69,70,63,64,65,62,60,61,423,424,425,422,420,421,429,430,431,428,426,427,126,127,128,129,130,131,124,125,123,120,121,122,661,665,664,673,399,401,400,397,398,396,407,405,406,403,404,402,417,418,419,416,414,415,408,409,410,411,412,413,380,378,379,383,381,382,375,376,377,374,372,373,391,392,390,394,395,393,389,387,388,385,386,384,90,91,92,93,94,95,88,89,87,84,85,86,672,678,681,686,588,590,589,593,591,592,596,594,595,599,597,598,605,603,604,601,602,600,611,609,610,607,608,606,163,164,162,166,167,165,161,159,160,157,158,156,177,178,179,176,174,175,168,169,170,171,172,173,16,17,15,12,13,14,22,23,21,18,19,20,695,700,699,703,30,32,31,35,33,34,27,28,29,26,24,25,499,500,498,502,503,501,497,495,496,493,494,492,512,510,511,515,513,514,507,508,509,506,504,505,524,522,523,527,525,526,519,520,521,518,516,517,286,287,285,282,283,284,277,278,276,280,281,279,683,691,690,696,574,573,575,572,570,571,564,565,566,567,568,569,530,528,529,533,531,532,536,534,535,539,537,538,542,540,541,545,543,544,548,546,547,551,549,550,561,562,563,560,558,559,552,553,554,555,556,557,288,289,290,291,292,293,294,295,296,297,298,299,662,666,663,675,615,617,616,613,614,612,623,621,622,619,620,618,633,634,635,632,630,631,624,625,626,627,628,629,647,645,646,643,644,642,638,636,637,641,639,640,649,650,648,652,653,651,655,656,654,658,659,657,51,52,53,50,48,49,57,58,59,56,54,55,682,693,692,697,37,36,38,39,40,41,42,43,44,45,46,47,319,320,318,322,323,321,317,315,316,313,314,312,1,0,2,3,4,5,6,7,8,9,10,11,147,148,149,146,144,145,153,154,155,152,150,151,140,138,139,143,141,142,135,136,137,134,132,133,671,685,677,689,365,364,363,360,361,362,370,371,369,366,367,368,324,325,326,327,328,329,330,331,332,333,334,335,337,338,336,340,341,339,343,344,342,346,347,345,350,348,349,353,351,352,356,354,355,359,357,358,77,75,76,73,74,72,83,81,82,79,80,78,694,701,698,702,456,458,457,461,459,460,464,462,463,467,465,466,473,471,472,469,470,468,479,477,478,475,476,474,98,96,97,101,99,100,104,102,103,107,105,106,117,118,119,116,114,115,108,109,110,111,112,113,482,480,481,485,483,484,488,486,487,491,489,490,660,668,667,674,190,189,191,188,186,187,180,181,182,183,184,185,194,192,193,197,195,196,200,198,199,203,201,202,206,204,205,209,207,208,212,210,211,215,213,214,227,225,226,223,224,222,218,216,217,221,219,220,303,304,305,302,300,301,309,310,311,308,306,307,669,680,676,687 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, M = {64} 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 20:02:06 · history