Equation 677 Database

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Magma 877e6c8437fd…

magma 877e6c8437fd
Size
381
Isomorphism class hash
877e6c8437fda3e798dbc5d06b541a17b1d5d247f7e7ecd72400f6aebd841d86
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 23:50:44
Display reorder
380,190,200,195,185,176,180,226,230,221,212,216,207,111,116,120,100,286,105,31,270,26,45,36,40,256,261,251,240,245,235,326,327,328,323,324,325,96,280,91,80,85,75,291,140,145,136,126,131,51,56,61,65,276,71,165,295,170,152,156,162,2,266,9,22,12,17,336,356,350,346,370,375,361,365,340,331,192,202,197,187,177,182,227,232,222,213,217,208,112,117,122,102,287,107,30,271,25,46,35,41,257,262,252,242,247,237,309,310,308,306,307,305,95,281,90,81,86,76,292,142,147,137,127,132,50,55,60,66,275,70,167,297,172,153,157,163,0,265,5,21,10,16,335,357,351,345,372,379,362,367,341,332,191,201,196,186,175,181,225,231,220,210,215,205,110,115,121,101,285,106,32,272,27,47,37,42,255,260,250,241,246,236,329,301,300,303,304,302,97,282,92,82,87,77,290,141,146,135,125,130,52,57,62,67,277,72,166,296,171,151,155,160,1,267,6,20,13,15,337,355,352,347,371,376,360,366,342,330,194,204,199,189,179,184,229,234,224,214,219,209,114,119,124,104,289,109,34,274,29,49,39,44,259,264,254,244,249,239,311,312,313,314,315,316,99,284,94,84,89,79,294,144,149,139,129,134,54,59,64,69,279,74,169,299,174,150,159,161,4,269,8,24,11,19,339,359,354,349,374,378,364,369,344,334,193,203,198,188,178,183,228,233,223,211,218,206,113,118,123,103,288,108,33,273,28,48,38,43,258,263,253,243,248,238,319,317,318,322,320,321,98,283,93,83,88,78,293,143,148,138,128,133,53,58,63,68,278,73,168,298,173,154,158,164,3,268,7,23,14,18,338,358,353,348,373,377,363,368,343,333 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 = {67} 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 23:50:45 · history