Equation 677 Database

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Magma b5401fa30670…

magma b5401fa30670
Size
381
Isomorphism class hash
b5401fa30670cf178ce9622aae530bc7ab43b61302ac9672d4f0e0a8fea360c7
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 23:29:41
Display reorder
380,101,112,106,129,119,124,56,54,55,258,57,58,293,52,53,51,49,50,152,157,147,137,142,132,249,254,244,234,239,229,204,209,199,219,224,214,194,92,93,91,94,90,309,310,311,306,307,308,172,162,167,187,177,182,262,273,268,295,278,281,289,99,98,96,97,95,359,348,339,374,352,344,364,332,367,377,100,110,105,125,116,121,31,29,30,256,27,28,292,23,48,24,25,26,154,159,149,139,144,134,245,250,240,231,236,226,201,206,196,215,220,210,190,35,36,34,32,33,329,327,328,326,324,325,174,164,169,189,179,184,260,271,265,299,275,284,286,4,5,0,2,3,355,347,335,370,354,340,363,334,369,376,104,113,109,128,118,123,76,77,75,259,79,78,294,74,73,71,72,70,151,155,146,135,140,130,247,252,242,232,237,227,202,207,197,217,222,212,192,63,64,62,60,61,319,320,318,322,323,321,171,161,166,185,175,180,264,274,269,297,279,282,287,68,69,65,66,67,357,349,337,372,350,342,361,330,366,379,103,111,108,127,117,122,20,21,22,255,1,59,291,15,16,19,17,18,150,156,145,136,141,131,248,253,243,233,238,228,203,208,198,218,223,213,193,82,83,81,84,80,316,317,315,313,314,312,170,160,165,186,176,181,263,272,267,296,277,280,288,89,88,86,87,85,358,346,338,373,351,343,360,331,365,378,102,114,107,126,115,120,12,10,11,257,13,14,290,46,47,45,43,44,153,158,148,138,143,133,246,251,241,230,235,225,200,205,195,216,221,211,191,7,6,9,37,8,300,302,301,304,305,303,173,163,168,188,178,183,261,270,266,298,276,283,285,42,41,39,40,38,356,345,336,371,353,341,362,333,368,375 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#6034e0b6e760ca1a616002bdffba2c9ecdf9d8efbd60a04eea2e11213baf5719, M = {69} 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 23:29:42 · history