Equation 677 Database

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Magma 7f4ecde3c4de…

magma 7f4ecde3c4de
Size
381
Isomorphism class hash
7f4ecde3c4de0b19aaf0c824f73c7f5785c4adbac1d6ffd32025ae511b8d3f14
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 23:31:10
Display reorder
380,162,135,176,187,1,16,86,96,306,310,200,212,241,247,251,232,236,36,46,41,121,110,276,266,62,67,50,152,140,146,165,170,181,191,9,285,11,21,75,81,102,92,308,307,311,309,206,195,222,216,225,25,291,156,127,131,116,105,282,256,272,262,72,57,295,30,351,345,331,355,361,375,335,341,371,366,163,138,178,188,3,15,88,98,303,300,203,213,243,248,253,233,238,37,47,42,123,113,278,268,63,68,53,153,143,148,168,173,183,193,5,286,10,20,78,82,103,93,305,304,302,301,208,198,223,218,228,27,292,158,128,133,118,108,283,258,273,263,73,58,298,32,352,347,330,357,362,376,337,342,372,367,160,137,177,185,2,17,87,95,317,312,202,210,240,245,250,230,235,35,45,40,120,112,275,265,60,65,52,150,142,147,167,172,180,190,6,287,12,22,77,83,100,90,316,315,313,314,207,197,220,215,226,26,290,155,125,130,117,107,280,255,270,260,70,55,296,31,353,348,332,358,363,377,338,343,373,365,161,136,175,186,0,18,85,97,319,323,201,211,242,246,252,231,237,38,48,43,122,111,277,267,61,66,51,151,141,145,166,171,182,192,7,288,13,23,76,80,101,91,318,320,321,322,205,196,221,217,227,28,293,157,126,132,115,106,281,257,271,261,71,56,297,33,350,346,333,356,360,379,336,340,370,368,164,139,179,189,4,19,89,99,327,325,204,214,244,249,254,234,239,39,49,44,124,114,279,269,64,69,54,154,144,149,169,174,184,194,8,289,14,24,79,84,104,94,329,328,326,324,209,199,224,219,229,29,294,159,129,134,119,109,284,259,274,264,74,59,299,34,354,349,334,359,364,378,339,344,374,369 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#75c864f1b3b5ca4c55a580191a279ecc912d7e894cd469271a5b5b9ceed20bb0, M = {71} 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 23:31:11 · history