Equation 677 Database

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Magma f11e2085266f…

magma f11e2085266f
Size
381
Isomorphism class hash
f11e2085266f3c4cdbe38178f1c5660cef0510f8fe630f9acae6732b18492ac8
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 23:34:25
Display reorder
380,37,31,26,270,46,41,316,317,315,313,314,312,265,20,15,7,12,110,100,105,285,115,121,292,127,132,137,142,147,160,152,155,172,167,277,72,67,57,63,51,91,96,85,76,81,180,186,177,196,200,190,205,211,215,222,227,232,246,236,241,262,252,297,2,280,257,335,372,350,367,332,377,355,340,345,362,36,30,28,273,48,43,300,302,304,306,308,310,268,23,17,8,13,113,103,108,288,118,123,291,126,131,136,140,145,163,150,158,170,165,276,70,65,56,61,53,93,98,88,78,83,183,187,176,197,203,193,208,212,218,221,226,231,248,238,243,261,251,296,3,283,256,338,370,353,366,331,376,358,343,348,361,38,33,27,271,45,40,328,329,327,325,326,324,267,22,16,6,11,111,101,106,286,116,120,293,128,133,138,143,148,162,153,157,173,168,278,73,68,58,62,50,90,95,86,75,80,181,185,178,195,201,191,207,210,216,223,228,233,247,237,242,263,253,298,1,281,258,337,373,351,368,333,378,356,341,346,364,35,32,25,272,47,42,320,318,319,323,321,322,266,21,19,5,10,112,102,107,287,117,122,290,125,130,135,141,146,161,151,156,171,166,275,71,66,55,60,52,92,97,87,77,82,182,188,175,198,202,192,206,213,217,220,225,230,245,235,240,260,250,295,0,282,255,336,371,352,365,330,375,357,342,347,360,39,34,29,274,49,44,305,301,303,311,307,309,269,24,18,9,14,114,104,109,289,119,124,294,129,134,139,144,149,164,154,159,174,169,279,74,69,59,64,54,94,99,89,79,84,184,189,179,199,204,194,209,214,219,224,229,234,249,239,244,264,254,299,4,284,259,339,374,354,369,334,379,359,344,349,363 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#890900158510c31f70f4fa8bc84bbffcea5cd35bea72b3996f708723e8ad424c, M = {76} 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 23:34:26 · history