Equation 677 Database

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Magma 8a18736b4816…

magma 8a18736b4816
Size
381
Isomorphism class hash
8a18736b481692e9fed3ad920d932748c49c6d4e7c8dea91333b42f8a58d519a
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 23:45:29
Display reorder
380,274,269,264,254,259,249,141,146,150,127,131,137,239,244,234,224,229,219,106,101,295,121,110,115,59,289,54,69,74,64,196,186,192,211,201,207,180,170,175,166,156,161,18,279,24,4,9,14,81,290,76,95,86,90,35,29,30,284,44,49,321,320,319,317,318,316,339,364,349,334,350,344,355,370,376,366,271,266,260,252,256,246,143,148,152,128,133,138,236,241,231,221,225,216,108,103,298,123,113,118,55,286,50,65,70,61,198,188,193,213,203,208,183,173,178,168,158,163,16,276,21,1,6,11,83,293,78,98,88,93,37,26,32,280,41,46,303,328,304,302,301,300,335,361,346,331,353,340,358,372,377,367,272,267,262,253,258,248,142,147,153,126,130,135,237,242,232,222,227,217,107,100,296,122,112,117,56,285,51,66,71,60,195,185,190,210,200,205,182,172,177,167,157,162,19,275,20,2,7,12,84,294,79,99,89,94,36,25,31,281,40,45,312,329,311,314,315,313,336,362,345,332,354,341,356,373,378,368,270,265,261,251,257,247,140,145,151,125,132,136,235,240,230,220,226,215,105,102,297,120,111,116,57,287,52,67,72,62,197,187,191,212,202,206,181,171,176,165,155,160,17,277,22,0,5,10,82,292,77,97,87,92,38,27,33,282,42,47,305,307,306,310,308,309,337,360,347,330,352,342,357,371,375,365,273,268,263,250,255,245,144,149,154,129,134,139,238,243,233,223,228,218,109,104,299,124,114,119,58,288,53,68,73,63,199,189,194,214,204,209,184,174,179,169,159,164,15,278,23,3,8,13,80,291,75,96,85,91,39,28,34,283,43,48,324,323,322,326,327,325,338,363,348,333,351,343,359,374,379,369 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#dba6afe67f86b36e533f777300b41b8ae8b2a840d4529c92a6cd7ab996e48d4f, 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 23:45:30 · history