Equation 677 Database

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Magma 0b292b304162…

magma 0b292b304162
Size
381
Isomorphism class hash
0b292b3041629cd1d0526ddb07c7cce60627cfa077d42dd2e6433a0fe44bdd07
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 23:29:49
Display reorder
380,187,182,177,197,201,192,32,21,25,43,38,268,139,143,149,128,293,131,303,304,305,301,300,302,68,58,63,53,273,48,17,16,288,113,118,123,163,168,173,298,153,158,15,279,14,79,84,73,98,103,108,88,283,93,241,236,246,250,255,260,226,221,230,205,210,215,343,363,368,347,358,370,330,353,375,338,185,180,175,196,202,191,31,23,27,40,35,266,136,140,145,126,290,132,320,318,319,323,321,322,65,56,60,51,270,46,8,1,286,110,115,120,160,166,171,296,150,155,0,276,2,75,80,70,95,100,106,85,281,90,243,238,248,253,258,263,227,222,232,207,212,217,340,360,366,345,355,372,333,351,376,336,186,181,176,195,200,190,30,22,28,41,36,265,137,141,147,125,291,130,308,306,307,311,309,310,66,55,61,50,271,45,6,7,285,111,116,121,161,165,170,295,151,156,9,277,5,77,82,71,96,101,105,86,280,91,242,237,247,251,256,261,225,220,231,206,211,216,341,361,365,346,356,371,331,350,379,335,188,183,178,198,203,193,34,24,29,42,37,267,138,142,148,127,292,133,316,317,315,313,314,312,67,57,62,52,272,47,12,13,287,112,117,122,162,167,172,297,152,157,10,278,11,78,83,72,97,102,107,87,282,92,244,239,249,254,259,264,228,223,233,208,213,218,342,362,367,348,357,373,334,352,377,337,189,184,179,199,204,194,33,20,26,44,39,269,135,144,146,129,294,134,329,327,328,326,324,325,69,59,64,54,274,49,18,19,289,114,119,124,164,169,174,299,154,159,4,275,3,76,81,74,99,104,109,89,284,94,240,235,245,252,257,262,229,224,234,209,214,219,344,364,369,349,359,374,332,354,378,339 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#6034e0b6e760ca1a616002bdffba2c9ecdf9d8efbd60a04eea2e11213baf5719, 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 23:29:50 · history