Equation 677 Database

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Magma 291fca2f3e69…

magma 291fca2f3e69
Size
381
Isomorphism class hash
291fca2f3e695b69787974d21b8d261e4b983bdf82cd4ba6305380708a677879
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 23:28:17
Display reorder
380,179,189,184,204,194,199,169,174,164,154,159,298,25,294,24,144,149,139,74,79,69,274,64,59,89,94,84,29,279,28,34,39,43,49,54,269,264,254,259,249,239,244,134,129,124,27,289,26,104,99,284,114,119,109,322,323,321,320,319,318,206,219,211,234,224,229,354,334,359,369,344,339,364,374,349,379,176,186,181,201,190,195,167,172,160,151,156,299,1,291,13,142,146,136,71,76,65,271,60,55,85,90,80,0,276,4,30,35,40,46,51,265,260,251,255,246,235,240,132,127,120,15,287,14,101,96,280,110,116,105,316,317,315,314,313,312,207,216,212,231,220,225,350,331,355,366,341,335,361,371,346,376,178,188,183,203,193,198,168,173,163,153,158,297,23,293,22,143,148,138,73,78,68,273,63,58,88,93,83,19,278,18,33,38,42,48,53,268,263,253,258,248,238,243,133,128,123,21,288,20,103,98,283,113,118,108,300,302,301,305,304,303,209,218,214,233,223,228,353,333,357,368,343,338,363,373,348,378,177,187,182,202,192,197,166,171,161,152,157,295,17,292,16,140,147,135,72,77,67,272,62,57,87,92,82,6,277,5,32,37,44,47,52,267,262,252,257,247,237,242,130,125,122,8,285,7,102,97,282,112,117,107,325,326,324,329,328,327,208,217,213,232,222,227,352,332,356,365,342,337,362,372,347,377,175,185,180,200,191,196,165,170,162,150,155,296,12,290,11,141,145,137,70,75,66,270,61,56,86,91,81,3,275,2,31,36,41,45,50,266,261,250,256,245,236,241,131,126,121,10,286,9,100,95,281,111,115,106,308,306,307,309,311,310,205,215,210,230,221,226,351,330,358,367,340,336,360,370,345,375 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#564914c332df918b1bab25ab6758cc0c591864f3f64c8c0ef251305010e22f83, M = {75} 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 23:28:18 · history