Equation 677 Database

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Magma a98d0a015c7b…

magma a98d0a015c7b
Size
381
Isomorphism class hash
a98d0a015c7be7b19eae4b899e92673e64265c4472cff0e7c34b8b85ba37bdf0
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 23:27:36
Display reorder
380,202,197,192,180,187,175,277,57,52,67,73,63,82,282,77,97,87,92,168,172,163,157,297,152,241,245,236,256,261,251,112,102,107,122,117,287,207,212,217,222,227,232,292,147,142,132,137,127,301,302,300,305,303,304,20,10,17,27,32,267,42,37,47,4,5,272,372,362,347,367,357,352,342,331,337,377,204,199,194,184,189,179,279,59,54,69,70,61,84,284,79,99,89,94,169,174,164,159,299,154,244,249,239,259,264,254,114,104,109,124,119,289,209,214,219,224,229,234,294,149,144,134,139,129,321,323,322,320,318,319,23,14,19,29,34,269,44,39,49,9,8,274,374,363,349,369,359,354,344,334,339,379,200,196,190,181,185,176,275,56,51,65,72,62,81,280,76,95,86,91,167,171,162,156,295,151,242,247,237,257,262,252,111,101,106,121,115,286,205,211,216,220,225,231,291,145,141,130,135,125,308,307,306,310,311,309,21,12,16,25,30,266,40,36,45,0,1,271,371,361,345,365,356,350,341,332,336,375,201,195,191,182,186,177,276,55,50,66,71,60,80,281,75,96,85,90,166,170,161,155,296,150,240,246,235,255,260,250,110,100,105,120,116,285,206,210,215,221,226,230,290,146,140,131,136,126,312,314,313,317,315,316,24,11,15,26,31,265,41,35,46,2,3,270,370,360,346,366,355,351,340,330,335,376,203,198,193,183,188,178,278,58,53,68,74,64,83,283,78,98,88,93,165,173,160,158,298,153,243,248,238,258,263,253,113,103,108,123,118,288,208,213,218,223,228,233,293,148,143,133,138,128,328,327,329,324,325,326,22,13,18,28,33,268,43,38,48,6,7,273,373,364,348,368,358,353,343,333,338,378 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 = {66} 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 23:27:37 · history