Equation 677 Database

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Magma d65a405c564f…

magma d65a405c564f
Size
381
Isomorphism class hash
d65a405c564f2976a628192fad27d8c9bd354adf081389c99c063d0f2cc66391
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 23:51:15
Display reorder
380,206,216,211,230,220,225,267,27,22,37,41,31,103,283,108,88,93,98,45,50,58,16,17,273,203,193,198,188,178,183,128,133,288,113,118,123,235,242,247,253,258,263,68,73,63,83,278,78,168,173,163,9,298,8,317,315,316,314,312,313,153,148,158,293,135,143,363,359,353,332,368,337,370,348,343,378,209,219,214,234,224,229,269,29,24,39,44,33,102,282,107,87,92,97,49,54,59,18,19,274,202,192,197,187,176,181,127,132,287,112,117,122,239,244,249,250,255,260,69,74,64,84,279,79,167,172,162,7,297,6,310,311,309,307,308,306,152,147,157,292,138,142,362,357,352,334,367,339,374,349,344,377,205,215,210,231,221,226,266,25,20,36,43,32,100,281,106,86,91,96,48,53,57,14,15,272,200,191,196,185,175,180,126,131,285,110,115,120,237,240,245,252,257,261,67,72,62,82,277,77,166,171,161,4,295,3,301,300,302,303,304,305,151,146,155,290,137,141,360,355,351,330,365,336,371,347,342,375,207,217,212,232,222,227,265,26,21,35,40,30,104,284,109,89,94,99,46,51,55,0,2,271,204,194,199,189,179,184,129,134,289,114,119,124,236,241,246,251,256,262,65,70,61,81,275,76,169,174,164,11,299,10,320,318,319,323,321,322,154,149,159,294,139,144,364,358,354,331,369,335,372,345,341,379,208,218,213,233,223,228,268,28,23,38,42,34,101,280,105,85,90,95,47,52,56,12,13,270,201,190,195,186,177,182,125,130,286,111,116,121,238,243,248,254,259,264,66,71,60,80,276,75,165,170,160,1,296,5,327,328,329,324,325,326,150,145,156,291,136,140,361,356,350,333,366,338,373,346,340,376 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#fac090d670a9c14492c148fae382a21bad3e48687c67df8555101af0e65e1711, M = {74} 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 23:51:16 · history