Equation 677 Database

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Magma b25e7f53d24d…

magma b25e7f53d24d
Size
705
Isomorphism class hash
b25e7f53d24dee59fa7d96f412c8bf4687887cd70ddb0a09e00b89de2aabc35e
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 19:46:31
Display reorder
660,33,420,471,491,490,472,31,492,493,421,470,419,32,489,488,423,474,36,497,496,424,475,34,498,499,422,473,35,495,494,486,418,28,469,487,416,29,467,482,483,417,30,468,484,485,27,414,465,478,479,25,415,466,481,480,26,413,464,476,477,682,679,684,683,52,249,182,196,177,183,53,197,175,247,181,248,54,198,176,252,185,51,195,180,250,186,49,193,178,251,184,50,194,179,202,244,58,188,172,245,59,189,203,173,246,60,187,204,174,57,243,191,201,171,55,241,192,199,169,56,242,190,200,170,665,666,669,670,207,264,396,383,408,397,205,384,409,262,395,263,206,382,407,260,399,210,386,411,261,400,208,387,412,259,398,209,385,410,381,255,213,394,406,253,211,392,379,404,254,212,393,380,405,216,258,390,377,402,214,256,391,378,403,215,257,389,376,401,676,681,677,675,78,620,622,621,623,630,76,628,631,629,614,612,77,613,615,644,646,74,645,647,652,654,75,653,655,636,638,73,637,639,605,606,84,604,607,590,82,588,589,591,598,83,596,597,599,80,573,572,576,577,81,582,581,580,583,79,326,325,1,327,700,698,704,703,0,284,347,371,459,348,2,372,460,285,346,283,3,370,458,287,350,4,374,462,288,351,5,375,463,286,349,6,373,461,369,282,7,345,457,280,8,343,367,455,281,9,344,368,456,10,278,341,365,453,11,279,342,366,454,12,277,340,364,452,691,692,694,693,118,144,334,265,149,335,119,266,150,142,336,143,120,267,148,140,337,117,268,145,141,338,115,269,146,139,339,116,270,147,271,135,109,332,155,133,110,333,272,156,134,111,331,273,154,112,138,328,274,151,113,136,329,275,152,114,137,330,276,153,662,661,671,672,132,563,562,305,105,565,130,306,103,564,560,561,131,304,104,569,568,128,301,108,570,571,129,302,106,567,566,127,303,107,311,558,123,559,100,554,121,555,312,101,556,122,557,310,102,126,550,551,307,99,124,553,552,308,97,125,548,549,309,98,695,696,689,690,314,539,538,359,23,541,315,360,24,540,536,537,313,358,22,545,544,317,362,19,546,547,318,363,20,543,542,316,361,21,357,534,320,535,14,530,321,531,355,15,532,319,533,356,13,323,526,527,353,17,324,529,528,354,18,322,524,525,352,16,685,686,674,673,64,626,627,625,624,635,65,633,632,634,619,618,66,617,616,650,651,63,649,648,658,659,61,657,656,642,643,62,641,640,609,611,70,610,608,594,71,595,593,592,603,72,602,601,600,69,578,579,575,574,67,586,587,585,584,68,438,439,425,388,701,702,697,699,159,447,233,514,515,234,157,517,516,448,232,446,158,512,513,450,229,162,520,521,451,230,160,522,523,449,231,161,518,519,510,445,165,239,511,443,163,240,506,507,444,164,238,508,509,168,441,235,502,503,166,442,236,505,504,167,440,237,500,501,664,663,668,667,290,95,433,217,37,434,291,218,38,96,432,94,289,219,39,91,436,293,220,40,92,437,294,221,41,93,435,292,222,42,223,86,296,431,43,87,297,429,224,44,85,295,430,225,45,299,89,427,226,46,300,90,428,227,47,298,88,426,228,48,680,678,688,687 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#a96a88e4cf05ff772a659e73be5ebad0179d3b86aa5fbe0be371d7ceb3ac096d, 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 19:46:32 · history