Equation 677 Database

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Magma 61279744a1b7…

magma 61279744a1b7
Size
381
Isomorphism class hash
61279744a1b7048a906d85ce168c0c48418001a78029f99f760da845067b05cf
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 23:23:01
Display reorder
380,110,121,115,131,126,285,254,259,264,239,244,249,96,86,91,106,100,281,14,19,269,23,29,34,138,143,293,153,158,148,274,44,39,54,59,49,218,208,213,233,223,228,279,64,69,74,79,84,178,183,188,193,198,203,323,321,322,320,318,319,298,7,6,168,173,163,355,349,363,373,351,368,378,337,344,334,114,124,119,134,129,289,253,256,261,235,240,245,99,89,94,109,104,284,12,17,267,21,27,30,136,141,290,151,155,146,273,43,38,53,58,48,216,206,211,230,220,225,278,63,68,73,78,83,176,181,186,190,195,200,314,312,313,317,315,316,295,3,2,166,170,161,359,348,360,370,354,365,375,339,343,331,112,122,117,132,127,287,250,255,260,237,242,247,97,87,92,107,102,282,10,15,266,24,25,32,135,140,291,150,156,145,272,42,37,52,57,47,215,205,210,231,221,226,277,62,67,72,77,82,175,180,185,191,196,201,304,305,303,300,302,301,296,1,0,165,171,160,357,347,361,371,352,366,376,335,342,330,113,123,118,133,128,288,252,258,263,238,243,248,98,88,93,108,103,283,13,18,268,22,28,33,137,142,292,152,157,147,271,41,35,51,55,46,217,207,212,232,222,227,276,60,65,70,76,81,177,182,187,192,197,202,306,307,308,309,310,311,297,5,4,167,172,162,358,346,362,372,353,367,377,338,341,333,111,120,116,130,125,286,251,257,262,236,241,246,95,85,90,105,101,280,11,16,265,20,26,31,139,144,294,154,159,149,270,40,36,50,56,45,219,209,214,234,224,229,275,61,66,71,75,80,179,184,189,194,199,204,327,328,329,324,325,326,299,9,8,169,174,164,356,345,364,374,350,369,379,336,340,332 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#45ae9dee612792667330602ba505951dcde187c4c1909cf40fbaf15f74e8af60, 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 23:23:02 · history