Equation 677 Database

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Magma 2f87f0c29f72…

magma 2f87f0c29f72
Size
381
Isomorphism class hash
2f87f0c29f725dff5a40671dd6c59ec74b34cf7cc482f6e233062024ab162e3c
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 23:37:06
Display reorder
380,289,282,299,269,279,209,199,204,194,184,189,274,124,129,133,139,144,149,113,114,229,115,111,112,314,315,316,311,312,313,174,179,169,159,164,154,104,219,105,101,102,103,100,96,97,214,98,99,254,259,264,239,244,249,294,118,119,117,234,116,110,107,106,109,224,108,349,339,369,359,344,354,364,334,379,374,288,283,298,268,278,207,197,202,192,182,187,273,123,128,130,138,143,148,52,53,225,49,50,51,302,301,300,329,303,304,172,177,167,158,163,153,41,215,40,38,39,37,5,6,7,211,36,4,252,257,262,237,242,247,292,27,30,29,232,28,2,3,0,48,221,1,346,336,368,357,340,350,362,332,377,372,287,281,297,265,275,206,196,201,190,180,185,270,121,127,131,136,141,147,69,70,227,67,71,68,306,307,305,309,310,308,171,176,166,157,162,152,60,217,61,57,58,59,56,8,9,212,54,55,250,255,261,236,241,246,290,25,26,24,231,23,63,64,62,66,222,65,347,337,367,356,342,352,361,331,376,370,286,284,295,266,276,208,198,203,193,183,188,271,120,125,132,135,140,145,89,90,228,91,87,88,319,317,318,322,320,321,173,178,168,155,160,150,80,218,81,77,78,79,76,72,73,213,74,75,253,258,263,238,243,248,293,94,95,93,233,92,86,83,82,85,223,84,348,338,365,358,343,353,363,333,378,373,285,280,296,267,277,205,195,200,191,181,186,272,122,126,134,137,142,146,14,15,226,16,17,18,323,324,325,326,327,328,170,175,165,156,161,151,10,216,42,11,12,13,33,31,32,210,34,35,251,256,260,235,240,245,291,20,19,22,230,21,44,45,43,47,220,46,345,335,366,355,341,351,360,330,375,371 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#9acf37934a26f07a9500b1ccb24642817fa617552582595ca38f94c8a1f3c019, M = {72} 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 23:37:08 · history