Equation 677 Database

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Magma 0889e7987e56…

magma 0889e7987e56
Size
381
Isomorphism class hash
0889e7987e56049b9f2df68c249dc61b8d7ad81867514863e29c22181438479a
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 23:25:51
Display reorder
380,8,7,9,10,11,6,298,263,268,163,273,288,14,15,16,17,12,13,278,283,293,198,158,153,28,29,24,25,26,27,238,243,248,253,258,232,0,2,3,4,5,1,312,313,314,315,316,317,183,188,193,168,173,178,223,228,203,208,213,218,19,21,23,20,22,18,341,368,372,340,358,342,338,339,378,362,106,105,107,102,103,104,297,262,267,162,272,287,113,108,109,110,111,112,277,282,292,197,157,152,100,101,96,97,98,99,237,240,246,251,256,231,117,118,119,114,115,116,300,302,303,304,305,301,182,187,192,167,172,177,221,226,200,205,210,215,91,93,95,92,94,90,354,365,370,333,355,351,350,343,377,360,56,55,57,58,59,54,299,264,269,164,274,289,30,31,32,33,34,35,279,284,294,199,159,154,53,48,49,50,51,52,239,244,249,254,259,234,41,36,37,38,39,40,326,327,328,329,324,325,184,189,194,169,174,179,224,229,204,209,214,219,47,43,45,42,44,46,334,369,373,344,356,335,332,330,379,363,68,67,69,70,71,66,296,260,265,161,271,286,86,87,88,89,84,85,276,281,291,196,155,151,81,82,83,78,79,80,235,242,247,252,257,230,73,74,75,76,77,72,321,322,323,318,319,320,180,185,190,165,170,175,220,225,201,206,211,216,62,64,60,63,65,61,348,366,374,346,357,349,347,345,376,364,132,137,133,134,135,136,295,261,266,160,270,285,138,139,140,141,142,143,275,280,290,195,156,150,128,129,130,131,126,127,236,241,245,250,255,233,149,144,145,146,147,148,307,308,309,310,311,306,181,186,191,166,171,176,222,227,202,207,212,217,123,125,121,124,120,122,337,367,371,336,359,331,353,352,375,361 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#50609e522fd5f79e53ac56beafcb5b424f2d261582798854b4ac2a2a84486b65, M = {69} 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 23:25:52 · history