Equation 677 Database

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Magma df9172da8848…

magma df9172da8848
Size
381
Isomorphism class hash
df9172da88487932fd29dc1c63cab8f73995edbdf8e42faa4e6aaf2325097d0e
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 23:36:58
Display reorder
380,239,249,244,234,229,93,94,289,1,0,189,224,278,284,299,264,269,274,124,114,119,108,99,104,17,15,16,251,13,14,199,204,194,214,219,209,306,307,308,309,310,311,129,134,139,144,149,154,92,91,259,90,88,89,179,184,174,164,169,159,290,8,9,10,11,12,345,354,359,334,369,341,374,339,379,364,238,248,243,233,228,86,87,288,18,19,188,223,277,283,298,261,266,273,123,113,118,109,95,100,74,77,73,254,75,76,198,203,193,213,218,208,301,300,302,303,304,305,128,133,138,143,148,153,83,84,258,48,49,85,178,183,173,163,168,158,294,80,81,79,82,78,349,353,358,333,368,344,373,338,378,363,237,247,242,232,227,70,71,287,72,69,187,222,279,280,295,262,267,270,122,112,117,106,97,102,35,36,34,252,38,37,196,202,191,212,217,207,329,327,328,326,324,325,127,132,137,142,147,152,45,46,255,42,43,44,177,182,172,162,167,157,292,39,40,41,3,2,347,352,357,332,367,342,372,337,375,361,236,246,241,230,225,52,53,285,50,51,186,220,275,281,296,263,268,271,121,110,115,105,98,103,55,54,58,253,56,57,195,200,190,211,216,206,320,318,319,323,321,322,125,130,135,141,146,150,68,67,257,66,64,65,175,180,170,161,166,155,293,62,63,61,59,60,348,351,356,330,365,343,371,336,377,360,235,245,240,231,226,31,30,286,33,32,185,221,276,282,297,260,265,272,120,111,116,107,96,101,27,25,26,250,28,29,197,201,192,210,215,205,316,317,315,313,314,312,126,131,136,140,145,151,4,5,256,6,7,47,176,181,171,160,165,156,291,24,23,21,22,20,346,350,355,331,366,340,370,335,376,362 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 = {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 23:36:59 · history