Equation 677 Database

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Magma 26a9d26063d1…

magma 26a9d26063d1
Size
381
Isomorphism class hash
26a9d26063d1b763d8fa33cb91a7e7d4f5fefba032b78ab8ef40c02e26076b95
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:31:33
Display reorder
380,290,295,322,141,131,129,142,288,323,296,130,294,308,143,289,273,145,307,281,127,274,146,279,325,128,144,275,326,280,126,123,282,277,136,272,124,283,278,137,270,125,284,276,135,271,122,299,140,291,286,120,297,138,292,287,298,121,139,293,285,149,147,134,132,133,148,372,349,379,348,374,373,371,354,351,350,240,248,318,96,114,115,97,241,319,246,113,247,324,95,242,254,100,320,259,110,252,98,260,321,111,99,253,306,258,112,109,263,255,91,265,107,261,256,89,266,108,262,257,90,264,105,249,92,244,267,106,250,93,245,268,251,104,94,243,269,101,102,117,118,116,103,378,345,376,331,370,369,355,352,347,346,173,178,302,23,13,11,24,171,303,179,12,177,301,25,172,156,27,328,164,9,157,28,162,300,10,26,158,314,163,8,5,165,160,18,155,6,166,161,19,153,7,167,159,17,154,4,150,22,174,169,2,152,20,175,170,151,3,21,176,168,119,0,16,14,15,1,375,353,363,336,362,364,361,338,337,339,207,184,304,29,47,48,30,208,305,185,49,183,327,31,209,193,33,315,198,46,194,34,199,316,44,32,192,317,200,45,42,202,197,55,189,43,203,195,53,190,41,201,196,54,191,38,188,56,180,206,39,186,57,181,204,187,40,58,182,205,37,35,50,51,52,36,367,343,365,342,377,368,366,341,340,344,211,216,310,64,82,80,62,212,311,217,81,218,309,63,210,225,65,313,233,78,226,66,231,329,79,67,227,312,232,77,74,234,229,87,224,75,235,230,88,222,76,236,228,86,223,73,220,60,215,238,71,221,61,213,239,219,72,59,214,237,69,70,85,83,84,68,356,330,359,335,358,357,360,334,333,332 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#7b9cbded8dea86ba89ad41a7d666a5c7106fc8964be53490042ed491416c85a9, M = {66} 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 23:31:34 · history