Equation 677 Database

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Magma cb4570e136c0…

magma cb4570e136c0
Size
381
Isomorphism class hash
cb4570e136c04dc40e5667870efc6d8151bf4c3c479735fad1fff4b9fd08bee5
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 23:35:36
Display reorder
380,13,8,3,268,22,16,326,324,325,329,327,328,270,26,31,36,40,45,63,51,57,276,65,70,280,76,81,96,85,91,121,286,115,106,111,101,130,291,125,146,136,141,159,164,154,299,174,169,199,204,194,184,189,179,224,229,234,209,214,219,238,243,248,253,258,263,374,340,336,378,346,369,361,333,356,350,10,5,0,265,21,15,322,323,321,319,320,318,272,27,32,37,42,47,61,52,56,277,67,72,282,77,82,97,87,92,124,289,119,109,114,104,134,294,129,149,139,144,158,162,153,297,172,167,198,203,193,183,188,177,222,227,232,208,213,218,235,240,245,250,255,260,372,342,337,379,347,367,364,330,359,352,14,9,4,269,24,18,315,316,317,312,313,314,274,29,34,39,44,49,64,54,59,279,69,74,284,79,84,99,89,94,122,287,117,107,112,102,132,292,127,147,137,142,156,160,151,295,170,166,196,202,192,182,186,176,221,226,231,207,212,217,239,244,249,254,259,264,371,344,339,375,349,365,362,334,357,354,11,6,1,266,20,17,310,311,309,307,308,306,273,28,33,38,43,48,62,53,58,278,68,73,283,78,83,98,88,93,120,285,116,105,110,100,131,290,126,145,135,140,155,161,150,296,171,165,197,201,191,181,187,175,220,225,230,206,211,216,236,241,246,251,256,261,370,343,338,376,348,366,360,331,355,353,12,7,2,267,23,19,301,300,302,303,304,305,271,25,30,35,41,46,60,50,55,275,66,71,281,75,80,95,86,90,123,288,118,108,113,103,133,293,128,148,138,143,157,163,152,298,173,168,195,200,190,180,185,178,223,228,233,205,210,215,237,242,247,252,257,262,373,341,335,377,345,368,363,332,358,351 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 = {76} 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 23:35:37 · history