Equation 677 Database

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Magma f20313153d3c…

magma f20313153d3c
Size
381
Isomorphism class hash
f20313153d3c9d0c738c2f95ad80a5e67a28bdfb287ad36ed68ba54b7c4863db
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 23:40:59
Display reorder
380,308,307,306,310,311,309,177,167,172,162,152,157,62,217,67,47,54,59,268,273,278,283,287,298,77,222,72,92,82,87,130,123,129,147,137,142,37,212,42,24,27,34,17,293,16,4,233,5,204,199,209,184,189,194,227,112,117,97,102,107,248,238,243,263,258,253,347,337,358,352,334,369,362,342,372,378,318,320,319,323,321,322,175,166,171,161,150,155,63,218,68,48,51,56,267,272,276,282,285,296,78,223,73,93,83,88,134,122,127,145,135,140,38,213,43,21,28,31,7,291,6,9,230,8,201,196,206,182,187,192,228,113,118,98,103,108,246,236,241,261,255,250,348,338,355,353,331,366,361,343,371,375,327,329,328,326,324,325,178,168,173,163,153,158,60,216,65,45,53,58,265,270,275,280,288,295,75,221,70,90,81,86,131,124,125,148,138,143,36,210,41,22,26,33,11,290,10,0,231,1,202,197,207,183,188,193,225,111,116,96,100,106,247,235,242,262,257,252,346,335,356,350,332,367,363,341,373,376,313,312,314,315,316,317,176,165,170,160,151,156,61,215,66,46,52,57,266,271,277,281,286,297,76,220,71,91,80,85,132,121,128,146,136,141,35,211,40,23,25,32,14,292,15,12,232,13,203,198,208,180,186,191,226,110,115,95,101,105,245,237,240,260,256,251,345,336,357,351,333,365,360,340,370,377,303,305,304,302,301,300,179,169,174,164,154,159,64,219,69,49,50,55,269,274,279,284,289,299,79,224,74,94,84,89,133,120,126,149,139,144,39,214,44,20,29,30,19,294,18,3,234,2,200,195,205,181,185,190,229,114,119,99,104,109,249,239,244,264,259,254,349,339,359,354,330,368,364,344,374,379 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#b1a8d3ba3db58654b282150679ccf1b928926281c9ba708fe38c950723e6a1aa, M = {75} 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 23:41:00 · history