Equation 677 Database

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Magma d7efcc0e0047…

magma d7efcc0e0047
Size
381
Isomorphism class hash
d7efcc0e004799c5985ab9cbe7a1868a6bfba9076abd26c47526cb7e99eabc2f
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 23:50:57
Display reorder
380,257,252,262,237,242,247,123,113,118,133,128,288,227,232,222,212,217,207,17,24,12,32,267,27,197,202,192,182,187,177,278,78,83,73,63,68,167,297,172,152,157,162,144,148,139,7,293,6,300,302,301,304,305,303,104,109,98,88,93,283,38,48,43,58,53,273,343,348,372,367,358,332,363,353,337,377,255,250,261,235,240,246,122,112,117,132,127,287,226,231,221,210,215,205,16,20,11,31,265,26,195,201,191,180,185,175,275,76,81,70,61,65,166,295,171,150,155,160,143,147,138,5,292,4,320,318,319,323,321,322,103,108,97,87,92,282,35,46,41,55,50,271,341,345,371,365,357,330,362,352,335,376,256,251,260,236,241,245,121,110,116,130,125,286,225,230,220,211,216,206,15,21,10,30,266,25,196,200,190,181,186,176,277,77,82,72,62,67,165,296,170,151,156,161,142,146,137,3,290,2,325,326,324,328,329,327,101,106,95,85,90,281,37,47,42,57,52,272,342,347,370,366,356,331,360,351,336,375,258,253,263,238,243,248,124,114,119,134,129,289,228,233,223,213,218,208,18,22,13,33,268,28,198,203,193,183,188,178,279,79,84,74,64,69,168,298,173,153,158,163,141,149,136,9,294,8,308,306,307,311,309,310,100,105,99,89,94,284,39,49,44,59,54,274,344,349,373,368,359,333,364,354,338,378,259,254,264,239,244,249,120,111,115,131,126,285,229,234,224,214,219,209,19,23,14,34,269,29,199,204,194,184,189,179,276,75,80,71,60,66,169,299,174,154,159,164,140,145,135,1,291,0,314,312,313,317,315,316,102,107,96,86,91,280,36,45,40,56,51,270,340,346,374,369,355,334,361,350,339,379 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#fac090d670a9c14492c148fae382a21bad3e48687c67df8555101af0e65e1711, M = {70} 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 23:50:58 · history