Equation 677 Database

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Magma a203a0176aaf…

magma a203a0176aaf
Size
595
Isomorphism class hash
a203a0176aaf9e0da2ebc2e50436345a7d617e2b9e6997fd221595c8c84cf195
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
2026-10-06 17:47:20
Display reorder
296,298,297,293,294,295,389,388,390,387,385,386,398,397,396,393,394,395,311,310,312,340,313,314,178,177,179,174,175,176,546,510,518,520,577,485,486,364,487,488,453,452,360,359,363,361,362,401,400,402,403,412,404,423,392,425,500,499,416,470,469,438,439,327,328,420,419,418,421,422,502,437,501,436,468,464,435,111,110,112,113,108,109,135,134,136,137,132,133,116,115,117,118,119,114,25,24,26,27,28,29,216,221,217,218,219,220,205,204,206,207,208,209,52,51,53,48,49,50,222,227,223,224,225,226,233,232,228,229,230,231,543,516,525,526,539,511,521,585,557,566,549,571,587,567,563,583,301,300,299,302,303,304,317,316,315,319,320,318,355,354,353,357,358,356,365,367,366,368,369,370,322,321,323,324,325,326,332,331,333,330,329,471,473,334,474,472,441,440,128,127,129,130,131,126,122,121,123,124,125,120,44,43,45,46,47,42,260,259,261,262,263,258,269,268,264,265,266,267,107,106,102,103,104,105,21,20,22,23,18,19,245,244,240,241,242,243,62,61,63,64,65,60,524,535,544,529,514,528,530,593,574,554,556,555,589,564,565,562,384,383,382,379,380,381,291,290,292,391,288,289,305,306,399,309,307,308,374,373,375,377,378,376,279,427,280,278,276,277,430,429,428,431,432,509,507,426,508,506,504,505,201,200,202,203,198,199,214,213,215,210,211,212,54,59,55,56,57,58,191,190,186,187,188,189,252,257,253,254,255,256,271,270,272,273,274,275,180,185,181,182,183,184,193,192,194,195,196,197,251,250,246,247,248,249,547,548,532,517,515,512,545,591,580,578,590,570,581,584,582,594,348,347,349,346,405,345,411,503,462,497,463,498,460,461,496,459,495,458,484,450,451,351,352,350,336,338,337,335,475,476,339,478,477,442,443,479,456,494,457,493,454,455,70,69,71,66,67,68,88,87,89,84,85,86,14,13,15,16,17,12,160,159,161,156,157,158,234,239,235,236,237,238,101,100,96,97,98,99,81,80,82,83,78,79,138,143,139,140,141,142,5,4,1,0,2,3,541,531,523,537,522,538,536,573,572,558,576,550,569,559,568,561,282,281,283,286,284,285,371,489,490,372,491,492,434,433,465,466,287,467,480,445,444,414,415,424,413,342,341,343,446,481,483,482,447,448,449,344,408,407,406,417,409,410,31,30,32,33,34,35,150,155,151,152,153,154,164,163,165,166,167,162,171,170,172,173,168,169,37,36,38,39,40,41,74,73,75,76,77,72,144,149,145,146,147,148,92,91,93,94,95,90,11,10,6,7,8,9,533,534,542,513,540,519,527,553,575,579,551,592,560,586,552,588 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#54e3a19f93137e404c924a9b37966faa8299b270c95916aef4ed0fa8730aa82d, M = the submagma generated by {0, 6} (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 2026-10-06 17:47:21 · history