Equation 677 Database

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Magma e097059dcb92…

magma e097059dcb92
Size
705
Isomorphism class hash
e097059dcb9226b861075ef2a2094104c80060053158ad33e6c945adba1bfc1b
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 15:09:34
Display reorder
660,334,151,353,360,528,332,152,354,361,529,333,150,355,359,527,337,154,352,356,524,155,335,350,357,525,336,153,351,358,526,340,149,344,366,534,338,147,345,367,535,339,148,346,365,533,145,343,347,362,530,146,341,348,363,531,144,342,349,364,532,674,683,673,685,378,45,492,99,402,379,46,493,100,403,377,43,491,101,401,374,37,488,98,398,38,375,489,96,399,376,40,490,97,400,384,56,498,105,408,385,58,499,106,409,383,55,497,107,407,49,380,494,104,404,50,381,495,102,405,52,382,496,103,406,670,663,662,666,504,281,480,390,456,505,282,481,391,457,503,283,479,389,455,500,280,476,386,452,278,501,477,387,453,502,279,478,388,454,510,287,486,396,462,511,288,487,397,463,509,289,485,395,461,286,506,482,392,458,284,507,483,393,459,285,508,484,394,460,675,679,682,681,239,72,540,303,450,240,73,541,304,451,241,74,539,302,449,238,75,536,306,446,76,236,537,307,447,237,77,538,305,448,645,78,649,646,648,653,79,657,654,656,636,80,641,638,640,81,613,615,616,617,82,621,625,622,624,83,629,633,630,632,698,700,703,704,275,156,21,414,324,276,157,22,415,325,277,158,23,413,323,274,159,20,410,320,160,272,18,411,321,273,161,19,412,322,266,162,12,420,330,267,163,13,421,331,268,164,14,419,329,165,269,15,416,326,166,270,16,417,327,167,271,17,418,328,691,690,694,689,36,61,297,546,564,39,62,298,547,565,41,60,296,545,563,42,64,300,542,560,65,44,301,543,561,47,63,299,544,562,48,67,295,552,570,51,68,293,553,571,53,66,294,551,569,70,54,291,548,566,71,57,292,549,567,69,59,290,550,568,669,671,664,661,195,122,214,596,597,193,120,215,598,599,194,121,216,594,595,198,125,213,217,192,123,196,211,591,590,197,124,212,592,593,201,128,205,609,608,199,126,206,611,610,200,127,207,607,606,131,204,208,601,600,129,202,209,603,602,130,203,210,604,605,696,695,693,692,138,35,582,426,438,139,33,583,427,439,140,34,581,425,437,141,31,578,422,434,32,142,579,423,435,143,30,580,424,436,136,26,588,432,444,137,24,589,433,445,135,25,587,431,443,29,132,584,428,440,27,133,585,429,441,28,134,586,430,442,677,678,684,687,557,228,576,372,230,558,229,577,373,231,559,227,575,371,232,556,224,572,368,233,225,554,573,369,234,555,226,574,370,235,650,219,651,647,644,658,220,659,655,652,642,218,643,639,637,222,618,619,614,612,223,626,627,623,620,221,634,635,631,628,697,699,701,702,116,87,516,308,259,114,88,517,309,257,115,89,515,310,258,119,86,512,311,255,84,117,513,312,256,118,85,514,313,254,111,93,522,314,265,112,94,523,315,263,113,95,521,316,264,92,110,518,317,261,90,108,519,318,262,91,109,520,319,260,668,672,665,667,3,252,468,173,183,4,253,469,171,184,5,251,467,172,185,2,248,464,169,182,249,1,465,170,180,0,250,466,168,181,9,243,474,179,189,10,244,475,177,190,11,242,473,178,191,246,8,470,175,188,247,6,471,176,186,245,7,472,174,187,686,676,688,680 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#05c0aaa7a3560fa146ae1951a40d178d675f2688aa4f7579703e2b967da3180b, 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 15:09:35 · history