Equation 677 Database

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Magma b4706b4c7c34…

magma b4706b4c7c34
Size
595
Isomorphism class hash
b4706b4c7c34209679a795f4944e710b54ca33bc65c0eb2ddb0821a37d8eaeb8
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 05:37:31
Display reorder
19,18,20,21,22,23,365,364,366,360,358,359,323,325,324,327,328,326,351,350,352,353,354,355,378,377,379,374,375,376,514,533,510,519,559,272,271,273,274,275,270,71,68,66,67,70,69,200,199,201,202,203,198,48,53,49,50,51,52,292,291,293,288,289,290,236,235,237,238,239,234,248,247,249,250,251,246,285,284,286,287,282,283,105,104,106,107,102,103,261,260,262,263,258,259,342,341,343,367,345,344,401,402,400,405,403,404,315,314,313,317,318,316,386,385,384,381,383,382,464,463,504,505,466,465,306,462,433,461,423,460,530,517,526,515,529,512,568,592,581,588,591,583,571,585,552,587,44,43,45,46,47,42,25,28,26,27,24,29,99,98,100,101,96,97,142,141,143,138,139,140,88,87,89,84,85,86,279,278,280,281,276,277,299,298,294,295,296,297,233,232,228,229,230,231,195,194,196,197,192,193,220,219,221,216,217,218,445,444,387,483,500,482,492,501,493,491,489,490,509,488,499,487,450,451,472,430,431,432,453,452,406,407,408,409,410,411,380,479,442,481,443,480,542,532,540,541,516,535,561,569,590,549,580,593,550,574,573,546,32,31,33,34,35,30,206,209,207,208,205,204,137,136,132,133,134,135,3,2,4,5,1,0,189,188,190,191,186,187,13,12,14,15,16,17,182,181,183,184,185,180,176,175,177,178,179,174,212,211,213,214,215,210,227,226,222,223,224,225,309,308,307,312,310,311,415,417,416,414,413,412,330,329,331,332,333,334,337,336,335,339,340,338,471,470,506,356,507,486,473,362,474,508,475,361,536,537,513,522,534,523,589,570,557,572,576,578,560,579,575,577,58,57,59,54,55,56,10,7,11,6,9,8,169,168,170,171,172,173,146,145,147,148,149,144,159,158,160,161,156,157,124,123,125,120,121,122,92,91,93,94,95,90,131,130,126,127,128,129,112,111,113,108,109,110,38,37,39,40,41,36,467,426,425,348,346,347,395,396,394,399,397,398,321,320,322,357,319,424,427,468,349,469,429,428,392,391,393,389,388,390,422,420,502,498,503,421,531,525,518,520,543,521,562,565,556,544,558,564,567,545,553,551,264,269,265,266,267,268,166,163,167,162,165,164,242,241,243,244,245,240,256,255,257,252,253,254,82,81,83,78,79,80,77,76,72,73,74,75,62,61,63,64,65,60,305,304,300,301,302,303,114,119,115,116,117,118,155,154,150,151,152,153,485,449,448,446,447,484,494,455,456,419,454,497,441,440,439,437,438,436,459,496,418,495,457,458,371,373,372,370,368,369,363,478,434,477,435,476,539,538,528,527,511,524,584,554,548,566,594,547,582,563,555,586 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#3cc60f474fc5309f8bfdc916c4fdc0ad032cdecf3f770b83999110b499ecb4f1, M = the submagma generated by {30, 72} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-07 05:37:37 · history