Equation 677 Database

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Magma b7bffa3f7a6f…

magma b7bffa3f7a6f
Size
705
Isomorphism class hash
b7bffa3f7a6f056d125b6ae40c2a922cca9e96efe5bbbc1dc899840c5d63cf42
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 20:10:23
Display reorder
660,357,393,78,570,546,79,358,571,547,394,80,395,359,572,548,392,77,356,569,545,390,75,354,567,543,391,76,355,568,544,561,384,348,84,537,562,385,349,85,538,563,386,350,86,539,387,564,351,83,540,388,565,352,81,541,82,389,566,353,542,685,676,687,679,269,4,125,405,277,123,267,406,278,0,124,2,268,407,276,10,121,265,404,280,6,122,266,402,281,8,120,264,403,279,396,11,275,116,283,397,7,273,114,284,398,9,274,115,282,3,399,271,119,286,5,400,272,117,287,118,1,401,270,285,669,661,665,664,468,31,288,417,522,289,469,418,523,32,290,30,470,419,524,34,291,467,416,521,35,292,465,414,519,33,293,466,415,520,408,29,459,294,513,409,27,460,295,514,410,28,461,296,515,25,411,462,297,516,26,412,463,298,517,299,24,413,464,518,683,682,680,674,639,638,64,640,643,65,647,648,651,646,63,654,655,656,659,630,67,631,632,635,614,68,615,616,619,622,66,623,624,627,444,227,224,70,587,445,225,222,71,585,446,226,223,69,586,588,590,589,73,592,598,600,599,74,603,72,607,608,606,611,704,697,699,701,492,203,241,187,369,242,493,188,370,201,240,202,494,186,371,199,244,491,190,368,200,245,489,191,366,198,243,490,189,367,193,209,483,247,360,194,207,484,248,361,192,208,485,246,362,205,196,486,250,363,206,197,487,251,364,249,204,195,488,365,690,691,693,689,321,441,132,480,534,133,322,481,535,442,134,443,323,482,536,440,135,320,479,533,438,136,318,477,531,439,137,319,478,532,471,432,312,130,525,472,433,313,131,526,473,434,314,129,527,435,474,315,126,528,436,475,316,127,529,128,437,476,317,530,671,662,668,666,54,102,212,153,504,210,55,154,505,103,211,104,56,155,506,101,215,57,152,503,99,213,58,150,501,100,214,59,151,502,159,108,52,218,495,160,109,53,216,496,161,110,51,217,497,107,158,48,221,498,105,156,49,219,499,220,106,157,50,500,692,694,696,695,582,429,304,345,558,305,583,346,559,430,303,431,584,347,560,428,300,581,344,557,426,301,579,342,555,427,302,580,343,556,336,420,573,310,549,337,421,574,311,550,338,422,575,309,551,423,339,576,306,552,424,340,577,307,553,308,425,341,578,554,686,688,675,681,637,636,166,641,642,167,644,649,650,645,165,653,652,657,658,628,162,629,633,634,613,163,612,617,618,620,164,621,625,626,509,60,113,172,510,507,61,111,173,511,508,62,112,171,512,594,595,593,168,591,597,601,596,169,602,170,605,609,604,610,702,698,700,703,236,21,38,456,333,36,234,457,334,22,37,23,235,458,335,20,41,239,455,332,18,39,237,453,330,19,40,238,454,331,447,12,231,44,324,448,13,232,42,325,449,14,233,43,326,15,450,230,47,327,16,451,228,45,328,46,17,452,229,329,663,672,667,670,148,174,89,261,381,87,149,262,382,175,88,176,147,263,383,177,92,144,260,380,178,90,145,258,378,179,91,146,259,379,252,180,139,95,372,253,181,140,93,373,254,182,138,94,374,183,255,142,98,375,184,256,143,96,376,97,185,257,141,377,678,677,673,684 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#bc84586c53073a7227d3f1cff463f9e10a3c0feadba644a539b68478442af133, 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 20:10:24 · history