Equation 677 Database

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Magma 91dbe8ead759…

magma 91dbe8ead759
Size
381
Isomorphism class hash
91dbe8ead7592a9226c30cb56f9f7b624f8b5638adf475a59481ddf3b9a138dc
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:29:57
Display reorder
380,242,297,247,237,225,230,132,123,128,147,137,142,202,207,197,188,192,183,106,111,115,96,101,290,46,50,47,48,49,212,275,285,270,262,267,257,59,57,58,61,252,60,282,54,55,56,220,16,162,151,156,177,167,172,316,315,317,312,313,314,51,217,52,53,15,14,337,332,377,347,367,350,342,362,357,372,243,298,248,238,228,233,133,121,126,148,138,143,203,208,198,189,193,184,107,113,118,98,103,293,67,71,68,69,70,213,278,288,273,263,268,258,62,63,64,65,253,66,283,75,76,77,221,0,163,150,155,178,168,173,318,320,319,323,321,322,72,218,73,74,8,9,338,333,378,348,368,353,343,363,359,373,244,299,249,239,229,234,134,124,129,149,139,144,204,209,199,185,194,180,108,114,119,99,104,294,2,3,80,78,79,214,279,289,274,264,269,259,90,91,92,93,254,94,284,88,89,87,224,86,164,154,159,179,169,174,301,302,300,305,303,304,83,219,84,82,85,81,339,334,379,349,369,354,344,364,358,374,240,295,245,236,227,232,130,120,125,146,136,141,201,206,196,186,190,181,105,112,117,97,102,292,22,23,24,25,26,210,277,286,272,260,265,256,18,19,17,21,251,20,280,36,37,35,223,34,160,152,157,176,166,171,328,327,329,324,325,326,10,216,33,13,11,12,335,331,376,345,365,352,341,361,355,370,241,296,246,235,226,231,131,122,127,145,135,140,200,205,195,187,191,182,109,110,116,95,100,291,6,4,5,27,7,211,276,287,271,261,266,255,42,43,41,45,250,44,281,38,1,40,222,39,161,153,158,175,165,170,311,310,309,307,308,306,31,215,32,30,28,29,336,330,375,346,366,351,340,360,356,371 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#6034e0b6e760ca1a616002bdffba2c9ecdf9d8efbd60a04eea2e11213baf5719, M = {73} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:29:58 · history