Equation 677 Database

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Magma 9bb51f868d71…

magma 9bb51f868d71
Size
381
Isomorphism class hash
9bb51f868d714e388cffaf1fce65e094b21e95619dbd37a068939f4b0d567478
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 23:27:27
Display reorder
380,37,30,44,7,329,55,14,48,1,25,26,31,38,42,8,323,56,12,49,0,24,32,36,43,6,324,54,13,50,2,46,322,23,16,39,57,5,27,9,35,47,320,21,17,33,40,58,3,28,10,45,321,22,15,34,41,59,4,29,11,18,19,52,53,51,20,340,342,341,375,356,368,334,355,374,357,183,208,190,220,327,201,227,197,213,238,239,209,184,191,221,301,202,225,195,214,237,207,185,189,219,300,203,226,196,215,192,313,236,229,188,206,218,211,222,181,193,303,234,230,182,186,204,216,212,223,194,302,235,228,180,187,205,217,210,224,231,232,198,199,200,233,360,369,358,343,361,362,345,344,359,376,132,128,139,169,311,121,176,146,162,158,156,126,133,140,170,312,122,174,144,163,157,127,134,138,168,310,120,175,145,164,141,319,153,178,137,123,167,160,171,130,142,309,154,179,131,135,124,165,161,172,143,318,155,177,129,136,125,166,159,173,151,152,147,148,149,150,378,346,363,365,379,377,335,347,364,370,119,112,94,89,314,105,64,101,82,75,76,113,117,95,87,317,106,65,99,83,77,111,118,93,88,328,107,63,100,81,96,315,73,66,92,110,84,80,62,114,97,316,74,67,115,90,108,85,78,60,98,326,72,68,116,91,109,86,79,61,71,69,102,103,104,70,338,373,333,372,331,354,339,367,366,332,279,275,286,252,306,268,259,293,248,241,242,273,280,287,253,307,269,260,291,246,240,274,281,285,254,308,267,258,292,247,288,304,265,261,284,270,250,243,257,277,289,305,266,262,278,282,271,251,244,255,290,325,264,263,276,283,272,249,245,256,298,297,296,299,294,295,371,330,336,337,352,349,353,351,350,348 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#5304aceb4265a7787eba18c077a38b00046b611d1328f1862a622a3aebcc3289, 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 23:27:28 · history