Equation 677 Database

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Magma a19872fe2e0a…

magma a19872fe2e0a
Size
705
Isomorphism class hash
a19872fe2e0ad04b0cd45eec4e639321b9768c46eebc4e69ce899aae08b70858
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 20:31:27
Display reorder
660,522,187,354,450,330,355,523,451,331,188,356,186,524,452,332,190,357,525,453,333,191,358,526,454,334,189,359,527,455,335,352,520,185,448,328,449,353,521,183,329,351,519,184,447,327,516,348,181,444,324,517,349,182,445,325,518,350,180,446,326,683,678,686,680,107,17,438,151,498,439,105,152,499,15,440,16,106,150,500,13,441,103,154,501,14,442,104,155,502,12,443,102,153,503,436,98,23,149,496,147,437,96,21,497,435,97,22,148,495,101,432,19,145,492,99,433,20,146,493,100,434,18,144,494,671,669,668,666,119,159,474,546,312,475,117,547,313,160,476,161,118,548,314,158,477,115,549,315,156,478,116,550,316,157,479,114,551,317,472,110,165,544,318,545,473,108,166,319,471,109,167,543,320,113,468,164,540,321,111,469,162,541,322,112,470,163,542,323,687,682,674,684,613,64,612,616,615,621,620,624,623,65,629,63,628,632,631,60,636,637,640,639,61,645,644,648,647,62,653,652,656,655,596,598,70,600,599,608,605,606,71,607,588,590,69,592,591,565,564,66,569,568,574,573,67,576,575,582,581,68,584,583,703,701,702,704,390,193,402,426,378,403,391,427,379,194,404,192,392,428,380,196,405,393,429,381,197,406,394,430,382,195,407,395,431,383,400,388,199,424,376,425,401,389,200,377,399,387,198,423,375,384,396,202,420,372,385,397,203,421,373,386,398,201,422,374,693,690,691,692,342,53,462,175,510,463,343,176,511,51,464,52,344,174,512,49,465,345,178,513,50,466,346,179,514,48,467,347,177,515,460,340,59,173,508,171,461,341,57,509,459,339,58,172,507,336,456,55,169,504,337,457,56,170,505,338,458,54,168,506,661,670,662,667,251,84,237,225,262,238,249,226,263,85,239,86,250,227,261,87,236,247,224,258,88,234,248,222,259,89,235,246,223,260,228,242,90,216,253,217,229,240,91,254,230,241,92,218,252,245,231,93,219,256,243,232,94,220,257,244,233,95,221,255,689,695,696,694,270,32,4,486,558,5,271,487,559,30,3,31,272,488,560,35,1,273,489,561,33,0,274,490,562,34,2,275,491,563,10,268,27,484,556,485,11,269,28,557,9,267,29,483,555,264,6,26,480,552,265,7,24,481,553,266,8,25,482,554,685,688,673,681,617,127,614,618,619,622,625,626,627,128,630,126,633,634,635,130,638,641,642,643,131,646,649,650,651,129,654,657,658,659,597,601,125,602,603,610,604,609,123,611,589,593,124,594,595,571,570,121,566,567,577,572,122,578,579,585,580,120,586,587,699,700,697,698,414,44,83,534,366,81,415,535,367,42,82,43,416,536,368,47,79,417,537,369,45,80,418,538,370,46,78,419,539,371,74,412,39,532,364,533,72,413,40,365,73,411,41,531,363,408,77,38,528,360,409,75,36,529,361,410,76,37,530,362,672,664,665,663,306,204,294,282,135,295,307,283,136,205,296,206,308,284,137,207,297,309,285,134,208,298,310,286,132,209,299,311,287,133,292,304,210,280,141,281,293,305,211,142,291,303,212,279,143,300,288,213,276,140,301,289,214,277,138,302,290,215,278,139,675,679,677,676 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#be22598f61f867b223264cf52ecf408910eea148415a700aef96392fba43b30a, 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 20:31:28 · history