Equation 677 Database

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Magma 4ad8b77fe6f5…

magma 4ad8b77fe6f5
Size
381
Isomorphism class hash
4ad8b77fe6f5d56c56cc7b2030ec8df8fbeadeba511a013141d671ada0489324
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 23:36:00
Display reorder
380,211,206,217,222,227,232,57,272,52,42,47,37,283,93,98,88,78,83,168,297,172,152,157,162,27,32,24,267,17,12,258,263,253,243,248,238,312,313,314,315,316,317,127,132,137,142,292,147,197,202,192,182,187,177,118,122,113,107,287,102,67,72,62,5,277,4,357,353,372,377,367,362,347,333,337,342,210,205,216,220,225,230,56,270,51,40,45,35,280,90,96,85,76,81,166,296,171,151,156,160,26,31,21,266,16,10,257,262,252,242,247,237,328,329,327,325,326,324,125,130,135,141,290,145,195,201,190,181,186,176,116,121,111,105,286,100,65,70,61,1,276,3,356,351,370,376,366,360,346,332,336,340,213,207,215,221,226,231,55,271,50,41,46,36,281,91,95,86,75,80,167,295,170,150,155,161,25,30,20,265,15,11,256,261,250,241,246,236,322,323,321,319,320,318,126,131,136,140,291,146,196,200,191,180,185,175,115,120,110,106,285,101,66,71,60,2,275,0,355,350,371,375,365,361,345,331,335,341,212,208,218,223,228,233,58,273,53,43,48,38,284,94,99,89,79,84,165,298,173,153,158,163,28,33,22,268,18,13,255,260,251,240,245,235,309,310,311,306,307,308,128,133,138,143,293,148,198,203,193,183,188,178,119,123,114,108,288,103,68,73,63,7,278,6,358,354,373,378,368,363,348,330,338,343,214,209,219,224,229,234,59,274,54,44,49,39,282,92,97,87,77,82,169,299,174,154,159,164,29,34,23,269,19,14,259,264,254,244,249,239,303,304,305,301,300,302,129,134,139,144,294,149,199,204,194,184,189,179,117,124,112,109,289,104,69,74,64,9,279,8,359,352,374,379,369,364,349,334,339,344 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#8e237b368ce49904371f47a0bbc192c3f49c4a8da81336b4c06fd9fdc3a5d75d, M = {72} 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 23:36:01 · history