Equation 677 Database

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Magma 5428f6da2b2d…

magma 5428f6da2b2d
Size
381
Isomorphism class hash
5428f6da2b2d35f214dc7133f5bcc475064ffe3e6fbde6853af3d50460034341
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 23:28:38
Display reorder
380,123,118,113,288,108,103,181,186,175,196,201,191,243,248,238,256,260,251,55,62,52,275,70,66,165,170,161,151,156,295,133,293,128,148,138,143,313,311,312,316,314,315,30,28,273,47,36,40,283,98,93,81,86,78,17,23,13,268,8,3,226,231,221,210,215,205,371,342,353,363,338,358,333,365,348,376,124,119,114,289,109,104,184,189,179,199,204,194,244,249,239,259,264,254,59,61,51,279,74,69,169,174,164,154,159,299,134,294,129,149,139,144,310,308,309,307,305,306,34,29,274,49,39,44,284,99,94,84,89,79,18,24,14,269,9,4,229,234,224,214,219,209,374,343,354,364,339,359,334,369,349,379,121,115,110,285,106,101,183,188,178,198,203,193,240,245,235,257,262,252,56,60,54,276,71,65,168,173,163,153,158,298,130,291,125,146,135,141,304,329,303,300,302,301,33,27,272,48,37,43,281,95,90,83,87,77,16,21,11,266,6,1,228,233,223,211,218,206,373,340,351,361,336,355,330,368,347,378,120,116,111,286,105,100,180,185,176,195,200,190,242,247,236,258,263,253,58,63,50,278,72,67,166,171,160,150,155,296,131,290,126,145,136,140,317,318,319,320,321,322,31,26,271,45,38,42,280,96,91,80,85,75,19,20,10,265,5,0,225,230,220,212,216,207,370,341,350,360,335,356,331,366,346,375,122,117,112,287,107,102,182,187,177,197,202,192,241,246,237,255,261,250,57,64,53,277,73,68,167,172,162,152,157,297,132,292,127,147,137,142,325,323,324,328,326,327,32,25,270,46,35,41,282,97,92,82,88,76,15,22,12,267,7,2,227,232,222,213,217,208,372,344,352,362,337,357,332,367,345,377 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#5a9d04a9c7b116e670149859ec35e9ea984c3e29c9284ef9fa55ee11860b9239, M = {68} 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 23:28:39 · history